Xiohun Xio, Lei Wng, Jun Xu,*, Xingfeng Lv, Pengfei Guo, Yishn Pn

a School of Mechanics and Engineering, Liaoning Technical University, Fuxin,123000, China

b School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing,100083, China

c School of Civil Engineering, Shaoxing University, Shaoxing, 312000, China

d College of Physics, Liaoning University, Shenyang,110036, China

Abstract To reveal the damage characteristics and catastrophic failure mechanism of coal rock caused by gas adsorption, physical tests and theoretical methods are employed. The results show that adsorption swelling can damage coal rock, which can be distinguished by fractal dimension. A fitting relationship between the adsorption damage and fractal dimension is proposed by experimental testing and theoretical analysis. High gas adsorption pressure proves to be the dominant factor that leads to coal failure softening and gas outburst disasters.Three main parameters concerning adsorption damage include the change rate of released energy density,the transition difference in the post-peak acoustic emission(AE)b value and the change rate of cumulative AE energy.Results show that all the three parameters present a step-type decreasing change with the increase in fractal dimension, and the fractal dimension shows a linear relationship within the same failure mode. Finally, a method is proposed to evaluate coal rock disaster transformation, based on the aforementioned three main parameters of adsorption damage.

2020 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords:Damage characteristics Catastrophic failure mechanism Adsorption damage Coal rock

1. Introduction

Coal rock is a porous medium with various pores and fissures,and gases are usually adsorbed and stored in these initial structures. In mining, evolution of the mechanical behavior between rock and gas is the main reason for dynamic coal mine disasters(Zhi and Elsworth, 2016; Hao et al., 2017; Jin et al., 2018). Viete and Ranjith (2006) conducted a standard uniaxial compression test on the coal samples to investigate the adsorption characteristics of CO2in coal rock mass. In their test, Australian lignite samples at room temperature with a diameter of 54 mm and a height of 108 mm were used, and a CO2gas pressure of 1.5 MPa was employed. The test results showed that the uniaxial compressive strength (UCS)and elastic modulus of the coal samples were reduced by 13% and 26%, respectively. Reucroft and Sethuraman (1987) studied the deformation characteristics of coal samples with a CO2adsorption pressure of 1.5 MPa and found that the adsorption led to a volume expansion of the coal sample, with an increase of 0.75%e4.18%.Karacan (2003) and Goodman et al. (2005) found that the adsorption of CO2on the coal sample caused an internal swelling phenomenon,which led to reordering of the internal structure with an increase in volumetric strain. In fact, the process of CO2adsorption in coal is complex, as CO2is not only adsorbed on the surface of coal rock but also dissolved in the coal matrix. With the release of gas and polycyclic aromatic hydrocarbons, the structure of the coal matrix, as well as permeability and stress level will be rearranged (Kolak and Burruss, 2006; Karacan, 2007; Wang et al.,2013a, b, 2015). Mehic et al. (2006) identified that adsorption could reduce the surface energy of coal rock, resulting in a reduction in tensile stress required for the initiation of new cracks in the coal rock. This indicates that adsorption process has substantial deterioration effects on the coal rock. Aziz and Li (1999), Perera et al. (2013) and Ranathunga et al. (2016a, b) studied the influences of adsorption pressure on the mechanical properties of the coal rock and found that adsorption caused coal matrix swelling and decreases in its strength and elastic modulus.Additionally,the influence of adsorption on the mechanical properties of coal largely depends on the gas pressure and phase behavior.

According to the previous studies,remarkable progress has been made in understanding the interaction between the gas and coal matrix in the adsorption process and the mechanical properties of coal rocks after adsorption. Nevertheless, investigations focusing on the damage characteristics and catastrophic failure mechanism of coal rock caused by gas adsorption are rarely reported. In addition,in deep mining,when the gas-bearing coal rock mass becomes unstable, it is easy to induce complex disasters with impact and outburst characteristics.

In this context, in order to analyze the damage characteristics and catastrophic failure mechanism of coal rock induced by gas adsorption, fractal characteristics of coal rock were used to understand the damage of gas-adsorbed coal rock, and stressestrain curves were adopted to analyze the relationship between energy dissipation and adsorption damage in the process of coal rock failure. By using acoustic emission (AE) monitoring in the whole process of coal sample loading, the relationship between the physical feedback signal and the damage parameter in the process of coal rock failure was explored,and the dynamic mining disaster mechanism was revealed.

2. Experimental set-up

2.1. Test system

The test system is composed of a fluid-solid coupling test system with coal rock adsorption multidirectional loading and an AE monitoring system. The fluid-solid coupling test system for coal rock adsorption multidirectional loading is a rigid electro-hydraulic servo press independently developed with a maximum load of 300 kN, load accuracy of 0.5% and maximum gas adsorption pressure up to 10 MPa. The multi-channel AE monitoring instrument SAEU2S is adopted for the AE monitoring system. The sampling frequency is set at 1000 kHz,the threshold values of the parameters and waveforms are both 40 dB, the gain of the main amplifier is 20 dB,and the sampling point is 1024.The test system is shown in Fig.1.

2.2. Specimen and test procedure

Raw coal specimens from the Sunjiawan coal mine (Fuxin,Liaoning Province, China) were selected. The dimension of the cylinder specimen is50 mm100 mm,and the evenness error of the top and bottom faces of the specimen is within0.02 mm, as shown in Fig. 2. The analysis results and maceral composition of pure coals are tabulated in Table 1.

Fig.1. Fluid-solid coupling test system.

Fig. 2. Coal specimens used in the uniaxial compression test.

The specific test procedure is described as follows:

(1) The airtightness of the device is important for accurate measurements. Before each test, the airtightness of the device should be checked. Helium at 6 MPa is injected into pressure chamber.If the reading of pressure gage is constant for 24 h, the device is considered airtight.

(2) After helium in pressure chamber is released, the coal specimen is sealed into the pressure chamber and then helium in pressure chamber is pumped out completely by vacuum pump.

(3) CH4is injected into the pressure chamber, and the gas adsorption pressure is set to 0 MPa,1 MPa,3 MPa and 5 MPa for saturated adsorption. After 24 h, the gas in the pressure chamber is released safely.

Additionally, before the compression test, the edge of loading system was tapped in order to ensure that the AE monitoring system has been connected properly. Displacement loading was adopted using a loading rate of 0.01 mm/s, a suggested rate to ensure static loading conditions in the experimental study of coal rock by Ulusay (2015). A high-speed camera and AE acquisition instrument were also used to record the failure process of coal rock, as shown in Fig. 1. It should be noted that all the tests in this investigation were conducted at room temperature (25C).

3. Test results and analyses

Table 2 gives the statistics of the mechanical parameters of the coal specimens in the tests.

3.1. Damage characteristics of gas-adsorbed coal specimens

As can be seen in Table 2,a total of four groups of specimens are designed with three specimens in each group, and specimens #2,#3,#8 and#11 are selected for analysis.Fig.3 presents the stresse strain curves of the four coal specimens with different gas adsorption pressures,and Fig.4 shows the failure modes of the four coal specimens.

In Table 2 and Figs.3 and 4,the related mechanical parameters and failure modes of the coal specimens change substantially after gas adsorption.One can see from Table 2 that the elastic modulus,peak stress and ratio of cumulative strain energy to residual strain energy decrease with increasing gas adsorption pressure, and it takes more time for the specimen failure with increasing gas adsorption pressure.

As can be seen from Fig. 3, with increase in gas adsorption pressure,the peak stress and elastic modulus of the coal specimens decrease gradually, and the post-peak residual strain presents anincreasing trend. In addition, the post-peak failure form changes from brittle failure to ductile failure with multiple stress drops. In Fig.4,when the adsorption pressure is zero,the failure of the coal specimen is characterized by splitting failure. When the gas adsorption pressure is 1 MPa (or 3 MPa), the failure of the coal specimen transfers from splitting failure to serious local failure.When the gas adsorption pressure reaches 5 MPa,the failure of the coal specimen shows features of fragmentation and crushing failure. These results indicate that the failure modes of the coal specimens are affected by the gas adsorption pressure.

Table 1Ultimate analysis and maceral composition of pure coals (Wang, 2004).

3.2. Calculation of damage to gas-adsorbed coal rock

It is assumed that the coal specimen is elastic in the process of gas adsorption, and the stressestrain relationship follows the Hooke’s law. After gas adsorption, the stresscan be replaced by the equivalent stressebased on the concept of stress equivalence as follows:

In light of the strain equivalence principle, we have

whereE0is the elastic modulus of the coal specimen without gas adsorption, and ε is the strain of the coal specimen. LetEDE01D, Eq. (2) can be rewritten as

whereEDis the elastic modulus of the adsorbed coal specimen.According to Eqs.(2)and(3),the damage variable of the adsorbed coal specimen can be written as

BecauseEDE0, the damage variableDcalculated by Eq. (4)ranges from 0 to 1. Accordingly, the damage variables of coal specimens#2,#5,#8 and#11 areD00,D10.33,D30.47 andD50.68, respectively. The higher the gas adsorption pressure is,the greater the damage variable is, and the smaller the elastic modulus (ED) is, which can also be found in Table 1.

3.3. Relationship between adsorption damage variable and fractal dimension

To study the adsorption damage of coal specimens from the perspective of the fractal dimension, the coal specimen fragments are screened using screening sizes of 0e2.5 mm, 2.5e5 mm, 5e 10 mm,10e15 mm,15e20 mm,20e30 mm,30e40 mm,40e50 mm and 50e100 mm, as shown in Fig. 5. The mass of coal specimen fragments at each size is weighed and recorded using a highsensitivity electronic scale. Table 3 lists the statistical results of the fragment distribution.

The relationship between the mass and size of fragments in Xie(1997) is introduced for the analysis,and it can be written as

The cumulative mass of fragments,total mass of each specimen and characteristic size of the coal specimen are calculated. After linear fitting, the relationship between the characteristic size and the mass of the coal specimen is obtained, and the fractal dimension of the coal specimen under different gas adsorption pressures is also displayed in Table 4.As shown in Table 4,with the increase in gas adsorption pressure,the average fractal dimension of damaged coal specimens increases from 2.16 to 2.43. Combined with the statistical data of fragment distribution in Table 3, it can be seen that for the coal specimens subjected to high adsorption pressure,the larger the fractal dimension is, the greater the number of fragments is, the smaller the fragment volume is, and the more obvious the failure softening characteristic is. The test results provide a means to understand the damage and failure characteristics of coal rock from the fractal dimension scale.

Based on the analysis in Section 3.2,ifE0andEDare measured,the damage variable of the coal specimen can be obtained,and the elastic modulus of the coal specimen in the uniaxial compression test can also be calculated approximately by

The elastic modulus of each coal specimen under different gas adsorption pressures calculated by Eq.(7)is substituted into Eq.(4)to obtain the damage variableD. Due to the correlation between damage variable and fractal dimension after coal specimen damage,the damage variableDof the coal specimen under different adsorption pressures is fitted with the fractal dimensiond(Eq.(8)),and the results are shown in Fig. 6.

wheremiandniare the fitting constants anddiis the fractal dimension of the coal specimen under different adsorption pressures.

From Fig.6 and Eq.(8),with increase in gas adsorption pressure,the damage variable of coal specimen shows a linear growth at the interval of different fractal dimensions.It suggests that the high gas adsorption pressure is the main factor that induces the gas outburst disaster, as the damage variable of coal specimen is related to the fractal dimension.

Table 2Statistics of related mechanical parameters of the coal specimens.

Fig. 3. Stressestrain curves of the coal specimens #2, #5, #8 and #11 with different gas adsorption pressures.

3.4. Energy release in the process of coal rock damage by adsorption

Fig. 4. Failure modes of the coal specimens #2, #5, #8 and #11 under different gas adsorption pressures.

In coal mining, instability disasters are closely associated with the energy released by the coal rock. With increasing gas adsorption pressure, coal rock is damaged, leading to changes in the accumulated elastic and residual energies. Therefore, the change rate of released energy density can be used to describe the release of energy in the process of coal specimen damage. The physical meaning is the release of energy per unit volume of coal rock within a unit time. By calculating the strain energy of the pre- and postpeak coal specimen, the theoretical expression of change rate of released energy density can be obtained.

本文在借鑒相關(guān)研究結(jié)果的基礎(chǔ)上，對當前湖南省城市化與生態(tài)環(huán)境的耦合協(xié)調(diào)發(fā)展階段與狀態(tài)進行研究分析，并提出了相關(guān)的改善措施，對推進湖南省新型城市化建設(shè)，提高省域內(nèi)城市化與生態(tài)環(huán)境協(xié)調(diào)度具有一定的借鑒意義。但由于城市化與生態(tài)環(huán)境內(nèi)部各要素之間交互耦合關(guān)系較為復雜，無論是在構(gòu)建指標體系方面，還是研究方法及模型運用等方面難免存在不足與缺陷，仍需深入研究。同時，關(guān)于城市化與生態(tài)環(huán)境耦合關(guān)系、相關(guān)性的研究方法還有很多[20]，如數(shù)據(jù)包絡分析法、德爾菲法、生態(tài)足跡法等等，本文由于數(shù)據(jù)限制，目前的指標體系還很難全面刻畫城市化與生態(tài)環(huán)境的全部內(nèi)涵，更為全面、合理的指標體系的構(gòu)建值得進一步探討。

According to the elastic theory, the formula of strain energy in the process of coal specimen deformation and failure can be written as

whereUis the strain energy,xis the axial stress in uniaxial compression,Sis the cross-sectional area of the specimen,andLis the amount of compression of the specimen.

Let εxL=Lbe the compression strain of the specimen andLbe the length of the specimen, Eq. (9) can be rewritten as

The strain energy densityUScan be written as

whereUSi1is the cumulative strain energy density of the coal specimen under gas adsorption pressure, andUSi2is the residual strain energy density.Therefore,the change rate of released energy density of a coal specimen can be written as

wheretis the total failure time after peak stress.

Fig. 5. Fragment sieving of the coal specimens.

According to the stressestrain curves of coal specimens under different adsorption pressures and the fractal dimension measured after failure, the fitting relationship between the change rate of released energy density and the fractal dimensiondis shown in Fig. 7:

wherefiis the change rate coefficient of released energy density,andgiis the initial value of the change rate of released energy density in fractal scale caused by gas adsorption damage.

One can see from Fig. 7 and Eq. (14) that high adsorption pressure accelerates the internal damage of coal specimens, and the failure process shows obvious characteristics of soft rocks.Through the analysis of fractal dimension,the released energy for a coal specimen is the lowest when the specimen fails, but the coal specimens with small particle sizes have strong softening properties. The low released energy in the failure process indicates that under high gas adsorption pressure, the coal specimen is fully damaged. Even if the energy instantaneously releases and induces the dynamic disaster, most of the gas outburst disasters are in the form of coal rock mass pressing or pouring, which will not lead to the dynamic failure of roof-coalfloor structure. In contrast, for the coal rocks without damage by gas adsorption, the overall mechanical properties of the coal rocks are good, the coal rock structure still has some bearing capacity after failure,and the released energy can transmit to the roof-coal-floor structure. Fig. 7 shows that under a certain adsorption pressure, the coal mine dynamic disaster induced by the instability of coal rock presents the combined characteristics of shock and outburst.

3.5. AE b value in the accumulated energy after peak stress

The deformation and failure processes of rock materials are often accompanied by the generation of signals such as sound,electricity and magnetism. The changes in emitted signals are directly related to the homogeneity and structural differences in the materials.The variation in the AEbvalue has a specific physical significance: as thebvalue increases, the amplitude of small AE events increases, and the coal rock failure is dominated by microfractures. When thebvalue is stable, the amplitudes of AE events are evenly distributed, and the distribution of micro-fractures at different scales in coal rock is relatively stable. As thebvalue decreases,the proportion of amplitude of AE events increases,and the failure possibility of large-scale block in coal rock increases. When thebvalue fluctuates within a small range,the coal rocks fracture in a form of progressive expansion.A decrease inbvalue within a wide range indicates that the coal rock will be destroyed (Xie, 1997).Therefore,according to the variation patterns in the AEbvalue,the instability state of coal rock can be determined, and then the occurrence mechanism of coal rock dynamic disaster can be revealed.

In order to calculate the AEbvalue of the coal rock, the Gutenberg-Ritcher formula can be modified as (Colombo et al.,2003):

where

whereais a constant; andAdBandAmaxare the maximum amplitudes of AE events in dB and microvolt, respectively. When calculating thebvalue, the least squares method is used, and the coal rock AE amplitude data can be statistically calculated usingAdB5 dB (Colombo et al., 2003).

The AE energy is the area under the signal detection envelope,which reflects the relative energy or intensity of the event generated in the failure process of the coal specimen.By analyzing every cumulative AE energy event, the instability degree of the coal specimen can be determined in a “sudden increase” scenario with respect to energy.The total cumulative AE energyQcan be written as

whereQiis the energy of each AE event.

During testing, by synchronously recording the signal of force-AE, the relationships of stress,bvalue and cumulative AE energy with time in the failure process of the coal specimen under different gas adsorption pressures are presented in Fig. 8.

In Fig. 8, when the gas adsorption pressure is lower, thebvalue before the peak stress is larger, and the decrease trend is obvious. The damage to the coal specimen is mainly dominated by the propagation of micro-cracks. With increasing adsorption pressure, in stage I, thebvalue decreases slowly, and in stage II, itsignificantly fluctuates (as shown in Fig. 8c). This suggests that the increasing adsorption pressure elevates the damage to the coal specimen. In stage III, the fluctuation of thebvalue is small,indicating that the damage degree of the coal specimen is weakened and the failure rate is reduced, as shown Fig. 7. In addition, from Fig. 8, it can be found that the variations in cumulative AE energy and stress show a good consistent correlation,which provides a feasible classification of coal rock dynamic disasters using multi-physical parameters. Therefore, the relationship of transition difference in post-peak AEbvalue and the change rate of post-peak cumulative AE energy with fractal dimension can be fitted, as shown in Figs. 9 and 10. In Figs. 9 and 10, with increase in gas adsorption pressure, the transition difference in post-peak AEbvalue and the change rate of post-peak cumulative AE energy show a stepwise decreasing trend in different fractal dimensions.

Table 3Distribution of the coal specimen fragments.

Table 4Statistics of the fractal dimension of the coal specimens under different gas adsorption pressures.

Fig. 6. Relationship between the damage variable D of coal specimen and the fractal dimension d.

4. Multi-physical parameters of cataclysm tendency induced by gas adsorption

In order to further study and analyze the multi-physical parameters of cataclysm tendency induced by gas adsorption, the damage variable, change rate of post-peak cumulative AE energy,transition difference in post-peak and change rate of released energy density are gathered and presented, as shown in Fig. 11. In Fig.11,when there is no gas adsorption,the fractal dimension varies from 2.1 to 2.2,and the coal specimens show the characteristics of splitting failure after compression tests.In view of the change rate in post-peak cumulative AE energy and transition difference inbvalue,the AE events mainly occur in the post-peak stage,where the cumulative AE energy has the largest change rate (approximately(2.5e2.54)105mV/ms),and the transition difference in post-peak AEbvalue is also the largest(approximately 0.51e0.54).In terms of release of energy,the change rate of released energy density of the coal specimen is the largest, and the post-peak released energy is rapid and intense. Through tests in a large range of coal rocks or coal rock mass, it shows that the coal rock has the most obvious impact tendency if the disaster occurs.

Fig.7. Relationship between the change rate of released energy density and the fractal dimension.

Fig. 8. Relationships of stress, b value and cumulative AE energy of coal specimens with time under different adsorption pressures:(a)0 MPa,(b)1 MPa,(c)3 MPa,and(d)5 MPa. I, II and III are the stages of crack propagation. In stage I, micro-cracks initiate and propagate. In stage II, stable and unstable cracks both propagate.

Fig. 9. Relationship between the transition difference in post-peak AE b value and fractal dimension d.

As the gas adsorption pressure reaches 1e3 MPa, due to the damage of gas adsorption, the fractal dimension is probably between 2.2 and 2.4. The number of large coal fragments decreases,the brittleness of coal failure is reduced, and the softening characteristics become stronger. The number of post-peak AE events increases, and the change rate of AE energy is probably between 1.7105mV/ms and 2.07105mV/ms.The transition difference inbvalue is probably between 0.3 and 0.42. From the perspective of energy dissipation, the change rate of released energy density decreases due to the softening effect of adsorption damage. Catastrophic disasters in mining usually have an impact-outburst composite tendency, which will cause damage to the surrounding coal rock mass or rock mass and supporting system when the disaster occurs,and they will also be accompanied by the outburst of a large number of coal fragments and gases.

Fig.10. Relationship between the change rate of post-peak cumulative AE energy and fractal dimension d.

Fig.11. Multi-physical parameter judgment of cataclysm tendency of coal rocks.

As the gas adsorption pressure reaches 5 MPa, the fractal dimensions are all greater than 2.4. When the coal specimen is broken, the numbers of fragmented and pulverized coal particles are the greatest,due to crushing failure.The longer the failure time is, the more obvious the softening effect will be from the change rate of post-peak cumulative AE energy andbvalue. Due to the increasing gas adsorption pressure, the damage of the coal specimen is significant,the intensity of post-peak damage is weakened,and the change rate of cumulative AE energy is the least (approximately (1.39e1.45)105mV/ms). In addition, with the influences of adsorption and swelling,the intensity of coal specimen failure,as well as the rate of failure,is reduced.The transition difference inbvalue is reduced to the minimum(approximately 0.18e0.2),and the change rate of released energy density is the lowest(approximately 6.16e7.28). Owning to the significant damage, the catastrophe occurs in a large range of coal rock masses,and a large amount of coal fragments and gas will gush out, with strong gas outburst characteristics.

5. Conclusions

Based on the fractal characteristics of coal rock damage caused by adsorption pressure,the experimental and theoretical methods are used to investigate the damage characteristics and catastrophic failure mechanism of coal rock. The relationship between the fractal dimension and the damage of coal rock, the change rate of released energy density,the transition difference in post-peak AEbvalue and the change rate of cumulative AE energy is established.The classification method of coal rock disaster types with multiphysical parameters is proposed. The main conclusions are drawn as follows:

(1) The damage and degradation of coal rock by adsorption swelling can be defined by fractal dimension. The fitting relationship between adsorption damage and fractal dimension shows that high gas adsorption pressure is the main influence factor that leads to coal failure, coal separation and gas outburst disasters.

(2) The results show that the change rate of released energy density of coal rock,the transition difference in post-peak AEbvalue and the change rate of cumulative AE energy show a step-type decreasing change trend with increasing fractal dimension.The linear relationship associated with the fractal dimension is suitable for characterizing the same failure type, which reveals the essence of coal mine dynamic disaster transformation from impact to outburst.

(3) A method is proposed to determine the transformation in the coal rock catastrophe type with the main characteristic parameters of adsorption damage, i.e. change rate of released energy density, change rate of post-peak AE energy andbvalue transition difference.

Declaration of Competing Interest

The authors wish to confirm that there are no known conflicts of interests associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Acknowledgments

The authors are gratefully acknowledged to the financial support by the National Natural Science Foundation of China (Grant Nos.51974186, 51774164 and 51774048).