Qingyi Tu ,Yunping Cheng *,Sheng Xue ,Ting Ren ,Xing Cheng

a State Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mines,Anhui University of Science and Technology,Huainan 232001,China

b Faculty of Safety Engineering,China University of Mining and Technology,Xuzhou 221116,China

c School of Civil,Mining & Environmental Engineering,University of Wollongong,NSW 2522,Australia

Keywords:Coal and gas outburst Intact coal Crushing work ratio Geological factors Outburst energy

ABSTRACT This research reviewed the mechanics and gas desorption properties of intact coal,and tested the crushing work ratios of different intact coals,and then,studied the stress conditions for the failure or crushing of intact coal and the gas demand for the pulverization of intact coal particles.When a real-life outburst case is examined,the required minimum stress for intact coal outburst is estimated.The study concludes that the crushing work ratios of three intact coal samples vary from 294.3732 to 945.8048 J/m2.For the real-life case,more than 2300 MJ of transport work is needed,and 10062.09,7046.57 and 5895.47 m3 of gas is required when the gas pressure is 1,2 and 3 MPa,respectively.The crushing work exceeds the transport work and even reaches 13.96 times of the transport work.How to provide such an enormous crushing work is an energy-limiting factor for the outburst in intact coal.The strain energy is needed for the crushing work,and the required minimum stress is over 54.35 MPa,even reaching 300.44 MPa.These minimum stresses far exceed the in-situ vertical and horizontal stresses that can be provided at the 300–700 m mining depth range.

1.Introduction

Coal and gas outbursts (hereafter referred to as outbursts) are an unexpected geological disasters for underground mines and represent the outcome of dynamic instability in the ground stress,the gas and coal within a coal seam under the combined effects of geological factors,mining activities and other factors [1,2].Large amounts of coal/rock and gas are injected into a mining space over a short time,causing enormous destruction and threatening the safety of production within the coal mine [3].However,due to the complexity and unpredictability of outbursts,the outburst mechanism is still not fully understood [4–6].

Hanes et al.[7]proposed that both stress and gas play an important role in outbursts,but one of them may play the dominant role for a specific outburst.Paterson [8] believes that outbursts represent the result of coal/rock structural instability under the action of a gas pressure gradient.Sato and Fujii [9] analyzed the seismic waves of a large-scale outburst in the Sunagawa Coal Mine and noted that an earthquake could have induced the outburst and played a major role in that particular event.Hu et al.[10,11] suggested that outbursts are a mechanical failure process that can be divided into four stages:preparation,triggering,development and termination.Hou et al.[12] believed that outburst is a violent disaster driven by released energy from gas desorption,and developed an instrument for the initial expansion energy of released gas measurement to predict outburst.Moreover,the spherical shell instability hypothesis proposed by Jiang and Yu dictates that coal failure under the effect of stress is the only necessary condition for outbursts,but crack expansion and shell instability under the effect of gas pressure are sufficient conditions for an outburst to occur [13,14].

These hypotheses focused on the driving factors,such as stress,gas,and seismic waves,all of which contribute to the occurrence of outbursts.However,coal is the predominant recipient for these driving factors,and thus,the properties of coal are also important for outbursts.In addition to the influences of vegetation,coalification,mineral species and mineral quantity[15]coal properties are affected by geological factors as well [16–18].After many years of mining activities,two typical types of coal,namely,structural coal and intact coal,are generally found in an initial coal seam.Structural coal is a kind of coal that is reconstructed from highly crushed or pulverized coal under the action of in situ stress.Structural coal has a very low strength and is easy to crush or pulverize again[16,17].The formation of structural coal is related to structural movements,including faulting,folding,thrusting,and rolling[19].In contrast,intact coal is not affected or is less affected by structural movements and thus maintains its primary structure with clear bedding and joints [20].Compared with structural coal,the strength of intact coal is very high,so intact coal is more difficult to crush or pulverize [21].

Dennis [22,23] proposed that most outburst incidents have been associated with abnormal geological conditions in Australian underground coal mines.Structural coal is usually considered to be closely related to outbursts,especially large-scale outbursts (outburst coal/rock mass ≥500 t),which has been verified by some outburst case studies [24,25].The high outburst risk of structural coal depends on its microscopic and macroscopic structures [26];and the mechanics and gas occurrence/flow properties of structural coal are favorable for the occurrence of outbursts[17,27,28].However,outbursts occurring in intact coal seams are seldom mentioned in the literature,and the energy-limiting factor and occurrence conditions for outbursts in intact coal seams have not been systematically studied.

This study reviews the mechanics and gas desorption properties of intact coal,tests the crushing work ratio of intact coal,and also summarizes some typical outburst characteristics to analyze the driving factors at different outburst stages.Then,this paper studies the stress conditions for the failure or crushing of intact coal and the gas pressure demand for the pulverization of intact coal particles.Moreover,a real outburst case is assumed to occur in intact coal seam,and the minimum stress condition for this case is estimated.Therefore,the energy-limiting factor and occurrence conditions for outbursts occurring in intact coal seams are studied,and the findings are helpful for judging the possibility of outbursts in intact coal seams at current mining depths.

2.Basic properties of intact coal

2.1.Strength properties and failure behavior of intact coal

Coal strength is an important parameter for determining its outburst risk [2].However,tests for coal strength have been performed using different coal samples,including irregular and regular samples.The intact coal strength has been tested by in situ methods and laboratory methods in the studies by Bieniawski and Van der Merwe [29,30].

Fig.1.Strengths determined from in situ tests on cubical coal specimens loaded under uniaxial conditions.

Generally,in situ tests were conducted underground using cubic samples with a size of 0.08–2 m [31].Fig.1 shows the in situ strengths given by two typical references.Bieniawski [29]tested the effect of the sample size on the coal strength and noted that the strength decreased from 33.6 to 4.4 MPa with increasing sample size,but the curve flattened out at a sample size of approximately 1 m.Moreover,Sheorey et al.[32] investigated that the in situ strength showed a definite downward trend with the buried depth.

For laboratory tests,coring specimens were commonly used[20].As reported in the studies by Okubo et al.[20,21,30,33–37],the coring specimens were tested at different diameters but with heights twice the diameter,as shown in Fig.2.Fig.2a shows that the measuring strengths of the coring specimens under uniaxial conditions are highly variable and range from 2.2 to 76.5 MPa.Fig.2b shows that with an increase in confining pressure,the specimen strength significantly increases.When the confining pressure is between 0 and 0.2 MPa,the strength of most specimens ranges from 10 to 30 MPa.

Fig.3 shows the typical stress–strain curve and failure pattern for intact coal from in situ and laboratory tests at different confining pressures.Both in situ and laboratory tests show that intact coal undergoes a significant elastic deformation before the stress peak,while the coal shows brittleness accompanied by a strength drop after the peak [38].Double pyramid-type failure was characteristic of the coal samples subjected to in situ testing,and this type of failure was invariably associated with the opening of vertical cleats and spalling from one or more faces;there usually remained a central block,even when all the loose coal pieces were removed[29].However,the failure was localized to a distinct shear band within the coal sample during the laboratory tests[39].Nevertheless,during both the in situ tests and the laboratory tests,all of the loose coal pieces were lumpy with irregular shapes and large sizes.

2.2.Gas desorption properties of intact coal

Coal is a porous medium with complex pores and fracture systems that provide spaces and channels for gas formation and migration.However,coal-forming processes result in the creation of different pore sizes and types,and many factors (such as vegetation,coalification,and geological factors) affect the pore structures of coal [16,18].Therefore,differences among pore structures cause variation in the gas formation and migration properties of coal.

The initial gas desorption capacity of coal is an important parameter for predicting the outburst risk [11].Lama et al.[2,40]suggested that the sorption/desorption rate in the first 30 s should be taken as the reference value.In addition,several parameters,including initial velocity of gas emission ΔP,gas desorption index Δh2,gas desorption index of drilling cuttingsK1,etc.,have been widely used in predicting the regional or localized outburst risk for coal mines,and these parameters reflect the initial gas desorption capacity of coal [2,41,42].

Fig.4 illustrates the average gas desorption rates of intact coal samples in the first 1 min under different gas equilibrium pressures [11,43–46].These coal samples come from different coalfields in China,such as the Huaibei Coalfield,Tiefa Coalfield,and Hedong Coalfield.The coal samples are ranked from low-rank lignite coal to middle-rank bituminous coal and to high-rank anthracite coal,and the coal particle size is 1–3 mm (following China National Standards AQ/T 1065–2008 and GB 474–2008).The results show that the gas equilibrium pressure is an external factor for the average gas desorption rate in the first 1 min.When the gas pressure is 1 MPa,the average gas desorption rate varies from 0.00147 to 0.03836 m3/(t.s).When the gas pressure is 2 MPa,the average gas desorption rate ranges from 0.002 to 0.04645 m3/(t.s);and the average gas desorption rate is<0.05705 and 0.06182 m3/(t s) when the gas pressure is 3 and 4 MPa,respectively.In addition,the coal rank is an intrinsic factor affecting the average gas desorption rate in the first 1 min[46].The average gas desorption rates of low-rank coal (lignite) and high-rank coal (anthracite) are usually higher than that of medium-rank coal (bituminous coal).

Fig.2.Laboratory tests of coal strength.

Fig.3.Typical stress–strain curve and failure pattern for intact coal.

Fig.4.Average gas desorption rates of intact coal samples in the first 1 min.

During the pulverization process,changes in the coal particle size affect the gas desorption property of coal [44].Some studies mention the existence of a critical size,which is usually at the millimeter scale or less[11,44,47].When the coal particle size is larger than the critical size,the initial gas desorption rate slowly decreases with particle size;however,when the coal particle size is smaller than this critical size,the initial gas desorption rate increases sharply as the size decreases.The critical size is mainly due to change in the gas diffusion path during the pulverization process [48].Considering the influence of inhomogeneity,Watanabe [49] obtained a modified relation between the particle size and initial gas desorption rate for coal.

where v1and v2are the initial gas desorption rates of coal particles,m3/(t.s),with corresponding particle sizes ofd1andd2,respectively;and ζ the correction factor.

To evaluate the effects of particle pulverization on the gas desorption capacity of coal,methane desorption experiments on intact coal samples with various particle sizes were conducted under different equilibrium pressures (0.5,1.0,2.0,and 3.0 MPa).The coal samples were collected from the 21coal seam in the Guhanshan Coal Mine in Henan province,China.The basic parameters of each coal sample are as follows:adsorption constanta=40.68 m3/t,adsorption constantb=0.71 MPa-1,proximate analysisMad=1.12,proximate analysisAd=13.41,and proximate analysisVdaf=12.88.The following six particle size ranges were selected:≤0.074,0.074–0.20,0.20–0.25,0.25–0.5,0.5–1,and 1–3 mm.

Fig.5 illustrates the average gas desorption rate in the first 1 min for each equilibrium pressure.With a decrease in the particle size,the gas desorption rate increases gradually,and the smallest particle (particle size ≤0.074 mm) demonstrates the largest initial rate.There are two desorption stages for these 6 particle size ranges.Among them,the 0.5–1 and 1–3 mm particle size ranges belong to the slow desorption stage,while the other 4 particle size ranges belong to the rapid desorption stage,showing that the gas desorption rate increases rapidly with a decrease in particle size.Next,the average particle size was used to represent the particle size in each range,the change in the gas desorption rate with particle size was fitted by Eq.(1),and the correction factor ζ and correlation coefficientI2were obtained;the results are listed in Table 1.

Fig.5.Average desorption rates in the first 1 min and the corresponding fitting curves.

2.3.Crushing work ratio test for intact coal

The crushing work needed for a unit of the newly added surface area,which is defined as the crushing work ratio,is a parameter reflecting the energy consumption in coal crushed or pulverized process [50,51].In this paper,a testing method is used to determine the crushing work ratio according to the coal particle compression test [26,52].This method is based on two assumptions:(1) coal particles are homogeneous and are considered spherical both before and after crushing and(2)the influence of particle size on the crushing work ratio is neglected.

This test was conducted using a TY8000-A uniaxial testing device manufactured by Jiangsu Tianyuan Test Equipment Co.,Ltd.There are two rigid platens in this device,where the upper platen can be moved by a servomotor driving the screw.The applied force is tested by a BAB-5MT or BAB-50MT load transducer,and the displacement is measured via a photoelectricity displacement coder.During the experimental process,a coal particle is placed between the lower and upper platens first.Then,the coal particle is compressed by moving the upper platen.When the upper platen senses the coal particle by a tiny force of 2×10-3N,the testing system starts to record the loading force and displacement of the platen.Moreover,a video microscope is also used to monitor the deformation of the coal particle during the experimental process.The photos for this equipment and similar experimental process have been introduced by Tu et al.[26].After each test,a force–displacement curve is plotted,and the crushing work performed on the coal particle is obtained by integrating the resulting curve[53].

wherewijis the crushing work of each test,J;Fthe applied force,N;andxthe displacement of the upper plate,m.Considering the discreteness of the tests,this study takes tens of coal particle samples with a completely spherical shape.Moreover,each coal particle is repeatedly compressed 3–5 times,ensuring that the coal particle is crushed.The total crushing work is obtained by the following equation.

Using standard sieves (i.e.,the Taylor system),the crushed intact coal samples are sieved to obtain the particle size distribution.Then,the newly added surface area is obtained by:

whereSiis the surface area of the coal particle in size rangei,m2;S0the surface area of the initial coal particle,m2;Gthe coal mass,kg;γithe mass proportion of coal particles in size rangei,%;dmthe average particle size,m;and ρ the density of coal,which is considered as a constant,kg/m3.Thus,the newly added surface area is:

where Γ is the crushing work ratio in size rangei,J/m2.

To test the crushing work ratio of intact coal,three intact coal samples with different Protodyakonov coefficientsfwere collected from three typical coal mines in China.In total,70–79 coal particles with a similar spherical shape were tested for each intact coal sample.The basic information of these coal samples and their particle size distributions after the tests are listed in Table 2.The particle sizes for most coal particles after the tests exceeded 1 mm,and the masses of coal in the 1–2,2–3,and 3–4 mm size ranges were much higher than those of the other particle size ranges.However,the mass proportion of ≤0.074 mm coal particles was very low,even though these coal particles did not appear after the QN coal sample tests.

Through the statistics of the crushing work and coal particle mass,the crushing work per unit mass of each coal particle was obtained.Furthermore,the total crushing work and total coal particle mass were obtained to calculate the average crushing work per unit mass of coal sample.Then,based on assumption that coal particles are homogeneous and are considered spherical both before and after crushing,the average particle size was used to represent the particle sizes in the ranges of 0.074–0.2 and 3–4 mm,and the average particle size of the ≤0.074 mm coal particles was 0.015 mm,which is consistent with the experimental results reported by Cai and Xiong[50].Therefore,the newly added surface area for each coal sample can be obtained by Eq.(5),and the crushing work ratio can be obtained by Eq.(6);and the results are shown in Table 3.

Table 1 Correction factor ζ and correlation coefficient I2.

Table 2 Basic information and particle size distributions after the tests.

Table 3 Results of the crushing work ratio tests.

Although discreteness exists in the data,the results show that there is a decreasing trend for the crushing work per unit masswith a decrease in the Protodyakonov coefficientfof the coal.The average crushing work per unit mass of the three coal samples changed from 636.1265 to 1641.7189 J/kg,while the crushing work ratio for these samples changed from 294.3732 to 945.8048 J/m2.The strongest coal sample (GHS) exhibited the highest crushing work ratio.

3.Coal and gas outburst and its energy source

In this section,the characteristics of outburst are analyzed,and the energy source of outburst is studied.

3.1.Characteristics of coal and gas outbursts

Since the first outburst accident was recorded in the Isaac Coal Mine,France,in 1834,tens of thousands of outburst accidents have occurred in over 19 coal-producing countries[1,25],including England,France,Hungary,Czechoslovakia,Belgium,Spain,Germany,Poland,Ukraine,Russia,South Africa,Turkey,Kazakhstan,Japan,New Zealand,Australia,America,Canada,and China.Although the geological backgrounds and mining conditions of these outbursts vary,these outbursts share similar characteristics.

An outburst is an instantaneous process accompanied by a strong dynamic effect.Generally,outbursts last only a few seconds or tens of seconds;e.g.,the Zhongliangshan Mine outburst,which occurred on November 4th of 1977 in Chongqing,lasted 39 s [54].Hundreds to thousands of tons of outburst coal [55] was ejected over a distance of approximately tens to hundreds of meters.Moreover,there is typically an outburst hole in the coal seam after an outburst,and this hole usually shows a characteristically small mouth and large cavity.Fig.6 shows the outburst holes of Bailongshan Mine outburst in September 2013 and Xinxing Mine outburst in November 2009,respectively.Due to differences among the outburst conditions,some outburst holes are clearly retained in the coal seam (Fig.6a),while some other outburst holes are partially or completely filled by outburst coal,as shown in Fig.6b.

In many cases,the outburst coal is highly crushed or pulverized,and the accumulation angle for the outburst coal is less than its angle of repose.Hu et al.[10] conducted an investigation of the coal particle compositions in several outbursts,and the mass distributions in different particle size ranges are shown in Fig.7.The outburst coal often contains a large fraction of ≤1.0 mm coal particles,accounting for more than 30%of all particles;pulverized coal,with a particle size of<0.1 mm,is also found in these outburst cases,accounting for 4.6%,3.6%,25.4%,4.3%,3.5%,6.6%,and 1.1%of all particles.Moreover,according to on-site investigations,there is an obvious zonal distribution of outburst coal/rock.

3.2.Energy source of coal and gas outburst

Similar to other physical processes,coal and gas outbursts undergo four stages:preparation,triggering,development and termination [4,6,54,56,57].

Based on the studies by Sobczyk et al.[58,59],coal crushing and transport are two necessary processes for an outburst.Generally,gas and stress provide the energy for these two processes,but the coal properties determine the energy demand[60].Coal crushing occurs during the preparation and development stages [54].Among them,the geological factors at the preparation stage and the presence of concentrated stress at the development stage cause the crushing of coal.During the crushing process,the stress is usually several times higher than the gas pressure,and the stress is commonly recognized as the primary contributor in this process,while the gas pressure can be neglected.In addition,the coal particles that have been crushed before will be pulverized again during the transport process.This phenomenon may be attributed to the collision of the coal particles [61,62],or so-called ‘‘popcorn”cracking induced by desorbed gas [63].

Coal transport occurs at the development stage,which provides the spatial conditions needed for the sustainable development of the outburst.When outburst coal is transported into the mining space,the coal will be free from stress;thus,gas will be the only factor affecting the transport process.The extremely fast initial gas desorption speed is the guarantee for the supply of outburst gas energy in a short time,which is one of the key factors determining the outburst risk difference of coals.

4.Stress conditions and gas demand for intact coal failure,crushing and pulverization

This section studies the stress conditions for the failure or crushing of intact coal and the gas demand for the pulverization of intact coal particles.The conclusions contribute to judge the crushing work source of outburst occurred in intact coal seam.

4.1.Stress conditions for intact coal failure

Fig.6.Outburst holes.

Fig.7.Quality ratio distribution of outburst coal in different cases [10,26].

The study by Liu et al.[64]indicates that the stress state for any underground position can be characterized by three principal stresses,and two of those principal stresses are situated in the horizontal plane for most areas.Additionally,the maximum horizontal principal stress,which is controlled by gravity stress and structural stress,is generally greater than the vertical stress in relatively shallow layers [65].Hoek and Brown [66] summarized 120 in situ stress measurement results from 10 countries to obtain the following linear relationship between the vertical stress and buried depth.

where σVis the vertical stress,MPa;andHthe buried depth,m.They also found that the ratio between the average horizontal stress and vertical stress lies within the limits:

where σHis the maximum horizontal principal stress,MPa;and σhthe minimum horizontal principal stress,MPa.Liu et al.[64] summarized 74 in situ stress measurement results from the Huainan Coalfield in the 350–1100 m depth range and obtained the following linear relationship between the vertical stress and buried depth.

As recorded in the studies by Beamish et al.[1,2],outbursts have occurred at depths as shallow as 80 m(Cezar Zofia Mine outburst in Poland,1894) and deeper than 1100 m (Yubari Mine outburst in Japan,1981).However,most of these outbursts occurred at depths ranging from 300 to 700 m.Using Eqs.(7)and(9),the estimated vertical stress in the 300–700 m depth range is 8.1–18.9 MPa.Moreover,the average horizontal stress in this depth range is 10–30 MPa on the base of statistical results.

Following the disturbance of mining activities or outburst behaviors,the initial stress balance of a coal seam is broken [67].Therefore,stress transfer occurs in front of the exposed surface,causing the formation of concentrated stress [67].Assuming that the initial stress is in a hydrostatic state,the radial stress (σrp)and tangential stress (σθp) in an area of plastic deformation can be expressed by the Mohr-Coulomb yield criterion [68–70].

wherecis the cohesion,MPa;φ the friction angle,°;andmand ε the intermediate parameters.After the peak of concentrated stress is reached,the radial stress (σrp) and tangential stress (σθp) gradually return to their initial state with an increase in the distance from the exposed surface.Elastoplastic theory holds that the peak point represents the boundary between the areas of elastic deformation and plastic deformation,which have:

Fig.8.Variation coefficients of the radial stress and tangential stress with the initial stress changes.

After considering the concentrated stress,the vertical stress is approximately 13.0–32.7 MPa in the 300–700 m depth range,while the horizontal stress is significantly unloaded in one direction.These stresses exceed the in situ strength of those cubic samples with a size larger than 0.3 m.Therefore,the stress conditions for intact coal failure can be satisfied in the depth range of 300–700 m.In addition,several dynamic events of intact coal,such as coal bump,coal burst,and pillar burst events,prove the failure of intact coal under the effect of stress[71,72].However,as observed in situ,all the loose coal pieces in these tests were lumpy with irregular shapes and large sizes;clearly,the particle characteristics of outburst coal are different,as shown in Fig.9a and b.

4.2.Stress condition for intact coal crushing

As shown in Fig.9b,outburst coal is highly crushed or pulverized.A large amount of crushing work is required to overcome the newly added surface energy,and the strain energy is the main source of this crushing work.Under a triaxial stress state,the strain energy of underground coal/rock can be expressed as studies by Hodot et al.[73,74].

whereEeis the strain energy per unit volume,MJ/m3;Ethe elastic modulus,MPa;and μ the Poisson’s ratio.Based on Eq.(13),the smaller the elastic modulus is,the larger the strain energy is.Therefore,considering that the elastic modulus of coal is much less than that of the surrounding rock,the strain energy mainly comes from the coal body.Based on the Heim’s hypothesis,the initial stresses are in hydrostatic state of stress,which are assumed that the stresses are equal in all three principal stress directions (σV=σH=σh),Eq.(13) can be simplified to:

Next,the newly added surface area of the unit volume of intact coal is analyzed after crushing.Meanwhile,changes in the coal density and initial surface area are neglected.Based on the assumption of spherical coal particles,the newly added surface area is:

where ΔS* is the newly added surface area of the unit volume of intact coal,m2;andd* the coal particle size after the crushing process,m.According to the test results in Section 2.3,three different crushing work ratios,namely,Γ=294.3732,Γ=378.3403,and Γ=945.8048 J/m2,are selected from three different intact coal samples.The elastic modulus and Poisson’s ratio of the intact coal samples are 2 GPa and 0.30,respectively [34].Thus,the newly added surface area and the stress demand for the crushing of intact coal are estimated by Eqs.(15) and (14).The newly added surface area and stress demand with changes in the coal particle size are shown in Fig.10.

With a decrease in the coal particle size,the number of coal particles quickly increases after the crushing of the unit volume of intact coal.Fig.10a shows that the newly added surface area rapidly increases with a decrease in particle size since the particle size is 5 mm or smaller.For example,when the particle size is crushed to 0.1 mm,the newly added surface area reaches 60000 m2,which is 100 times that when the particle size is crushed to 10 mm.

In addition,more crushing work is required for an increase in the newly added surface,which necessitates additional strain energy.Fig.10b shows that the stress demand for the crushing of intact coal rapidly increases with a decrease in particle size when the particle size is <5 mm.When the particle size is crushed to 0.1 mm,the stress demands corresponding to the three types of intact coal with different crushing work ratios are 242.64,275.08,and 434.93 MPa.

4.3.Pulverization of intact coal caused by gas

Outburst coal particles will be pulverized again during the transport process,which are driven by gas.The collision of the coal particles and the ‘‘popcorn”cracking induced by desorbed gas dominate this pulverization process.

Fig.9.Size characteristics of coal after coal burst and outburst.

Fig.10.Relationship between the coal particle size and newly added surface area or stress demand.

4.3.1.Effect of collision on the pulverization of coal particles

The collision between coal particles or between coal particles and roadways (barriers) induces localized loading,which results in significant plastic failure at the impact site followed by the pulverization of coal.Similarly,based on the assumption of homogeneous spherical coal particles,the collision process can be simplified as shown in Fig.11.The collision process begins at the point of contact between the coal particles or between the coal particle and roadway(barrier),and thus,an infinite collision stress is provided at the contact point.However,with the plastic failure of the coal near the contact point,the loaded surface gradually increases,causing the collision stress on the loaded surface to decrease.When the collision stress on the loaded surface σζis equal to the compression strength of the coal particle σc,the plastic failure stops.Therefore,the missing part of the spherical coal particle is considered to be the pulverization zone caused by a collision (Fig.11).

Based on momentum theory by Warsi[75]the localized loading on the loaded surface is:

Fig.11.Schematic of the impact process for coal particles.

whereFcis the localized loading on the loaded surface,N;tζthe collision time,s;Δpthe momentum change of the coal particle,kg.m/s;σζthe collision stress on the loaded surface,MPa;Rthe radius of the coal particle,m;and β the opening angle of the loaded surface,°.When the stop condition of pulverization is satisfied with σζ=σc,the opening angle of the loaded surface can be obtained by Eqs.

(16) and (17);thus,the volume of the pulverization zone can be expressed by:

whereVζis the volume of the pulverization zone,m3;and σcthe compression strength of the coal particle,MPa.During the collision process,the pulverization rate is:

Next,the changes in momentum before and after the collision are discussed.For the case of a collision between coal particles(Fig.11a),the collision condition is that the velocity of the rear coal particle v1is greater than the velocity of the front coal particle v2.Assuming that the coal particles have the same velocity after the collision and ignoring any changes in the particle masses,the momentum change is approximately as follows:

wherem1is the mass of the rear coal particle,kg;andm2the mass of the front coal particle,kg.Eq.(20) shows that the momentum change is closely related to the relative velocity between the two coal particles before the collision.However,these collided coal particles are usually transported in the same direction and with a similar velocity,suggesting that the momentum change is very small.

For the case of a collision between a coal particle and a roadway(barrier),the coal particle stops after the collision,as shown in Fig.11b.The momentum change can be expressed as:

where vζis the velocity of the coal particle,which is generally 10–50 m/s,as recorded in the studies by Tu et al.[54,76,77].Moreover,Dong et al.[52] tested the compression strength of 1–3 mm intact coal particles to be 2–5 MPa.Setting the collision time to 0.01 s and the radius of the coal particle to be within 2–10 mm,the pulverization rate of the collision between a coal particle and roadway(barrier)is calculated by Eqs.(16),(19),and(21).The pulverization rate is 0.0002%–0.6638%,which demonstrates that the pulverization rate of intact coal particles is very low for this case.Similarly,considering that the momentum change is very small,the pulverization of intact coal particles caused by the collision between coal particles may also be limited.

4.3.2.Effect of ‘‘popcorn”cracking on coal particle pulverization

During the transport process,the concentration gradient between the interior and surface of a coal particle drives the diffusion of desorbed gas[43].Based on the gas diffusion model[78]the variation in the gas concentration within the coal particle is:

whereCis the gas concentration within the coal particle,mol/m3;Dthe gas diffusion coefficient,m2/s;τ the diffusion time,s;Pmthe gas pressure within the coal particle,MPa;Tthe thermodynamic temperature,K;andRidthe ideal gas constant,Rid=8.31441 MPa.m3/(-mol.K).A variation in the gas concentration causes a change in the gas pressure,which results in the formation of a gas pressure gradient between the interior and surface of the coal particle.This gas pressure gradient has a tension effect on the coal particle,and thus,the coal particle is pulverized at the position where the gas pressure difference exceeds the tensile strength of the coal particle [4].

wherePmiis the gas pressure at a certain position within the coal particle,MPa;Pm0the atmospheric pressure at the surface of the coal particle,MPa;and σtthe tensile strength of the coal particle,MPa.

Eq.(23) shows that the pulverization of a coal particle caused by gas desorption depends on the gas pressure difference and the tensile strength of the coal particle.Using the numerical simulation method,Wang[79]found that the gas pressure difference between the interior and surface of a coal particle gradually decreases with increasing time,while the largest gas pressure difference occurs at the initial time.However,compared with the initial gas pressure of the coal seam,the gas pressure is greatly reduced at the beginning of the transport process.

Moreover,although the tensile strengths of intact coal particles are seldom recorded,the tensile tests conducted on intact coal specimens indicate that the tensile strength of most specimens exceeds 1.0 MPa[20,80,81];thus,the tensile strength of intact coal particles may be even higher if the influences of cracks and bedding planes on the tensile strengths of the specimens are considered.Therefore,the particle pulverization caused by ‘‘popcorn”cracking requires an extremely high gas pressure within the coal seam.

4.3.3.Verification of intact coal particle pulverization

Based on the theory of similarity,Jin[77]designed a new apparatus to simulate the transport of outburst coal in a roadway,and also focused on the pulverization effect of intact coal particles during the transport process.The test results can be used to verify the pulverization of intact coal particles during the transport process.

By using 1–3 mm intact coal particles collected from the No.10 coal seam of the Wolonghu Mine in China,CO2and N2tests were conducted under a 0.5 MPa gas pressure.According to the results,the pulverization rate (the mass of<1 mm coal particles vs.the total mass of transported coal) in the CO2test was 8.15%,while the pulverization rate in the N2test was 3.06%.In addition,the particle size distribution of the pulverized coal indicated that the coal hardly to be pulverized to particle sizes <0.2 mm,as shown in Fig.12.In particular,the mass rate of<0.074 mm coal particles accounted for 5.02% of the pulverized coal and 0.41% of the total transported coal for the CO2test,while the mass rate of<0.074 mm coal particles accounted only for 1.46% of the pulverized coal and 0.045%of the total transported coal for the N2test.

Fig.12.Particle size distributions of pulverized coal [77].

Considering the influence of gas adsorption on the pulverization of coal particles[82,83],the pulverization effect increases with the adsorption amount of gas.The magnitude of the pulverization effect caused by CH4may be between that of the pulverization effect caused by CO2and that of the pulverization effect caused by N2.That is,the pulverization rate caused by CH4will be<8.15%,while the mass rate of<0.074 mm coal particles will be<0.41% under a 0.5 MPa gas pressure.Therefore,it can be demonstrated that the pulverization rate of intact coal particles during the transport process is very low,especially for<0.074 mm coal particles;alternatively,an extremely high gas pressure is required to cause a large amount of intact coal particle pulverization.

5.Stress conditions for the occurrence of an outburst in intact coal—a real case calculation

5.1.A brief review of the Xinxing Mine outburst

On November 21,2009,an extra-large outburst occurred in the No.15 coal seam in the Xinxing Coal Mine,China.This accident occurred in an area of geological fracturing,which is controlled by a large fault;furthermore,there was a magmatic intrusion near the outburst at a distance of approximately 7–18 m from the floor of the No.15 coal seam.The depth of the outburst position was 394 m.

Approximately 3845 tons of outburst coal/rock are ejected,including 1697 tons of coal and 2148 tons of rock.As shown in Fig.13,the outburst coal/rock was ejected over a distance of 317 m,including 278 m along the exploration roadway,34 m along the south crosscut of the No.3 level,and 5 m along the return air roadway.There was an obvious zonal distribution of the outburst coal/rock.Along the exploration roadway,in the range of<11 m,the roadway was piled up with large rocks;in the range of 11–113 m,the roadway was filled with rock to a filling height of approximately 1.6–2.9 m;and in the range of 113–278 m,the highly crushed or pulverized coal was mainly packed with a packing height of 1.1–1.7 m.Moreover,highly crushed or pulverized coal was distributed along the south crosscut of the No.3 level and the exploration roadway with packing heights of 0.9–1.8 and 0.3–1.5 m,respectively.

5.2.Calculation of particle size distribution for outburst coal

Transporting thousands of tons of outburst coal/rock costs a great deal of transport work,which requires sufficient gas [11].Assuming that only horizontal displacements exist,the entire distribution length of the outburst coal is divided into several small segments,as shown in Fig.14.Therefore,the transport work in each segment can be expressed by:

whereWtis the total transport work,MJ;Wtithe transport work of segmenti,MJ;mithe outburst coal mass of segmenti,kg;lithe distance from the outburst position,m;fmthe friction coefficient;gthe acceleration due to gravity,m/s2;and α the coal seam angle,°.

As noted in Fig.14,the boundaries are determined by the supply of adsorbed gas volume.

Gas contributes to outbursts by the release of expansion energy.When the gas pressure changes from the initial gas pressureP1to the atmospheric pressureP2,the gas energy is expressed as:

whereEgis the gas energy,MJ;Vthe gas volume,m3;Vfthe free gas volume,m3;Vathe adsorbed gas volume,m3;and κ the adiabatic coefficient.The free gas is stored in the fracture system and exists in the gas phase,making it immediately available to participate in the outburst.

where φ is the coal porosity,%;andVmthe coal volume,m3.However,the adsorbed gas participating in the outburst is more complex,and it should first desorb and change into free gas.Based on the analysis of the gas desorption capacity affected by the pulverization process in Section 2.2,the coal particle size has a great influence on the gas desorption.The adsorbed gas volume can be expressed as:

Simplifying the distribution of outburst coal/rock in the Xinxing Mine outburst,the natural bulk densities of outburst coal/rock in different segments are considered to be equal,and the influences of roadway intersections on the transport of outburst coal are neglected.Then,the mass of outburst coal/rock in each segment is estimated according to the packing height,and the total transport work is obtained by Eq.(25).

A limited selection of studies show that the initial coal seam gas pressure for most outburst cases is<3 MPa;therefore,initial coal seam gas pressures of 1,2,and 3 MPa are selected for the case calculation.Based on the calculation of total transport work,the gas volume demand for the transport of outburst coal/rock is calculated by Eq.(26).Thus,the free gas volume and the adsorbed gas supply volume are obtained by Eq.(27).The calculation parameters are collected in Table 4,and the calculation results are listed in Table 5.The results show that more than 2300 MJ of transport work is required for the transport of thousands of tons of outburst coal/rock.When the initial coal seam gas pressure is 1,2,and 3 MPa,the gas volume demand is 10062.09,7046.57,and 5895.47 m3,respectively.However,the contribution of free gas only accounts for a small part of the gas volume demand,while most of the gas comes from adsorbed gas.

Table 4 Calculation parameters [54,73].

Certain amounts of coal particles with particle sizes less than the critical size are required to supply the adsorbed gas.Based on the analysis in Section 4,the stress dominates the failure and crushing of intact coal under the selected gas pressure,while the pulverization of intact coal particles during the transport process can be neglected.Referring to the coal particle size distribution in Fig.9,the particle size distribution of the Xinxing Mine outburstis also divided into 5 particle size ranges,that is,<0.1,0.1–1.0,1.0–5.0,5.0–10,and >10 mm.

However,considering that<1.0 mm coal particles play a decisive role in the supply of adsorbed gas,the mass ratio of<0.1 mm coal particles is set asX,the mass ratio of coal particles in the 0.1–1.0 mm particle size range is set asY,and the mass ratio of coal particles in the other three particle size ranges is (1-X-Y)/3.Additionally,the mass ratio of each particle size range should be reasonable,and thus,the mass ratiosYand (1-X-Y)/3 are consistent with the statistical results in Fig.9.According to the adsorbed gas volume in Table 5,the particle size distribution of outburst coal should be satisfied.

whereMis the mass of outburst coal,t.Moreover,the particle size of coal in each size range is characterized by the average particle size except for the greater than 10 mm particle size range,for which the particle size is simplified to 10 mm.However,due to the lack of initial gas desorption data for this outburst case,the upper limit for the average gas desorption rate in Fig.4 is used to calculate the average gas desorption rate of the coal particles in the 5 particle size ranges when the initial coal seam gas pressure is 1,2,and 3 MPa.The correction factor ζ is 0.55,which refers to the experimental results in Table 1.In addition,the outburst timetis 1 min.After choosing the parameters,the upper limit for the gas desorption capacity of the outburst coal is estimated,and the particle size distribution for outburst coal is solved by Eq.(29)according to the linear programming method.As shown in Fig.14,the value range of the mass ratio for<0.1 and 0.1–1.0 mm coal particles is located in zone (1) when the gas pressure is 1 MPa;when the gas pressure is 2 MPa,the value range corresponds to zones (1) and (2);when the gas pressure is 3 MPa,the value range corresponds to zones(1),(2),and (3).

5.3.Estimation of the minimum stress for the occurrence of an outburst in intact coal

Based on Eq.(15),the total newly added surface area can be expressed as:

There is an optimal solution of the total newly added surface area according to Eq.(30) and the value ranges in Fig.14.PointsA,B,andCcorrespond to the minima of the total newly added surface area when the gas pressures are 1,2,and 3 MPa,respectively.The mass ratios in different particle size ranges are listed in Table 6,and the minima of the total newly added surface area are 34704619.71,9464962.40,and 3648887.93 m2.

Three different crushing work ratios,namely,Γ=294.3732,Γ=378.3403,and Γ=945.8048 J/m2,are selected from three different intact coal samples.Then,the minimum crushing work and minimum stress for the occurrence of an outburst in intact coal are calculated,as listed in Table 7.The results show that a large amount of crushing work is required for the occurrence of an outburst in intact coal.Generally,this crushing work exceeds the transport work of outbursts and even reaches 13.96 times the transport work.Meanwhile,it is estimated that the minimum stress is 167.61–300.44 MPa when the gas pressure is 1 MPa;whenthe gas pressure is 2.0 MPa,the minimum stress is 103.41–185.37 MPa;and when the gas pressure is 3.0 MPa,the minimum stress is 54.35–97.42 MPa.

Table 5 Results of the different energies involved in the Xinxing Mine outburst.

Table 7 Minimum crushing work and minimum stress.

6.Discussion of the energy-limiting factor for the occurrence of outbursts occurred in intact coal

Coal failure and transport are two of the necessary processes for outbursts.Due to the adsorbed gas supply demand,outburst coal needs to be highly crushed or pulverized.In particular,certain amounts of coal particles with particle sizes less than the critical size are required to supply the adsorbed gas.However,the mechanical properties of intact coal necessitate an immense amount of crushing work for an outburst to occur in intact coal.Generally,the amount of crushing work exceeds the transport work of outbursts and even reaches several times of the transport work.Accordingly,it is an energy-limiting factor for the occurrence of an outburst in intact coal to provide such an enormous amount of crushing work.

Coal crushing occurs at the preparation and development stages.Among these two stages,the geological factors at the preparation stage and the concentrated stress at the development stage cause the crushing of coal,and the stress is recognized as the primary contributor in these processes,while the coal particles that have been crushed before will be pulverized again during the transport process.However,as the analysis in Section 4.3 shows,the pulverization rate of intact coal particles during the transport process is very low;alternatively,an extremely high gas pressure is required.Therefore,strain energy provides the most crushing work,and thus,stress plays an important role in the occurrence of outbursts in intact coal.

Nevertheless,based on the real case calculation,when the initial coal seam gas pressure is 1–3 MPa (the initial coal seam gas pressure for most outburst cases),the minimum stress for the occurrence of an outburst in intact coal is over 54.35 MPa,even reaching 300.44 MPa.These minimum stresses far exceed the vertical and horizontal stresses that can be provided at current mining depths.Therefore,the probability of an outburst (especially a large-scale outburst) occurring in intact coal is very low under the in situ stresses at the 300–700 m mining depth range.It is commonly accepted that outbursts at these mining depth are related to geological factors,such as faulting,folding,thrusting,and rolling[2].That is,these structural movements cause the coal seam occurrence state to transform over long-term geologic history,leading to the crushing or pulverization of intact coal [25,84].

7.Conclusions

(1) Intact coal has a high strength and shows brittleness accompanied by a strength drop after the stress peak.The crushing work ratios of three intact coal samples with different Protodyakonov coefficientsf(0.59–1.57)were tested by the coal particle compression test,and the crushing work ratio changed from 294.3732 to 945.8048 J/m2.

(2) After considering the concentrated stress,the stress conditions for intact coal failure can be satisfied in the depth range of 300–700 m.However,with decreasing coal particle size,the number of coal particles quickly increases after the unit volume of intact coal is crushed,and the stress condition for intact coal crushing also rapidly increases.When the particle size is crushed to 0.1 mm,the stress demand exceeds 242.64 MPa.During the transport process,the pulverization of intact coal particles caused by particle collision and ‘‘popcorn”cracking is very low;alternatively,an extremely high initial coal seam gas pressure is required.

(3) For the real-life case calculation,more than 2300 MJ transport work is needed for the transport of outburst coal/rock.Furthermore,10062.09,7046.57,and 5895.47 m3of gas is required to supply the necessary transport work when the gas pressure is 1,2 and 3 MPa,respectively.The minimum total newly added surface area is 34704619.71,9464962.40,and 3648887.93 m2,respectively.

(4) An immense amount of crushing work would be required for an outburst to occur in intact coal.The crushing work exceeds the transport work and even reaches 13.96 times of the transport work.How to provide such an enormous crushing work is an energy-limiting factor for the outburst in intact coal.The strain energy is needed for the crushing work,and the required minimum stress is over 54.35 MPa,even reaching 300.44 MPa.These minimum stresses far exceed the in-situ vertical and horizontal stresses that can be provided at the 300–700 m mining depth range.

Acknowledgements

The authors are grateful for the support from the National Natural Science Foundation of China (Nos.52004008 and 52004005),Natural Science Foundation of Anhui Province of China(Nos.2008085QE260 and 2008085QE222),and a Project is supported by Independent Research fund of The State Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mines (Anhui University of Science and Technology)(No.SKLMRDPC19ZZ07).