Catastrophic mechanism of coal and gas outbursts and their prevention and control

Availableonlineatwww.sciencedirect.comMININGELSEVIER° SciencedirectSCIENCE ANDTECHNOLOGYMining Science and Technology 20(2010)0209-0214Catastrophic mechanism of coal and gas outburstsand their prevention and controlLI Shugang. ZHANG Tianjuncollege of Energy, Xi'an University of Science and Technology, Xi'an 710054,China2college of Science, Xi' an University of Science and Technology, Xi'an710054.chinaAbstract: Based on the engincering observations of coal and gas outbursts during mining processes and the experimental resultwe built a thin plate mechanical model for layered and spalled coal bodies. We studied the mechanical mechanism of outbursts, dueto instability, of thin plates of coal rocks under the action of in-plane load and normal load, by using the catastrophe theory. Thetotal potential function is derived for the layered rock system, the cusp catastrophe model for the system is established. the bifurca-tion set that makes the system unstable is given, the process in which gradual change of action forces leads to catastrophic changeof state is analyzed, and the effect of movement path of point(P, q)in the control space on the stability of rock plate is analyzedThe study results show that during the process of coal mining, the stability of the layered coal bodies depends not only on itsphysical properties and dimensions but also on the magnitudes and changing paths of the in-plane load and the normal load. whenthe gas in the coal bodies ahead of the mining face is pre-drained, the gas pressure can be reduced and the normal load g can belowered. Consequently, disasters such as coal and gas outbursts can be effectively preventedKeywords: coal and gas outbursts: catastrophe theory; instability1 Introductionmechanisms, the phenomena can be analyzed moredeeply and many new and meaningful results can beIn China, during mining processes, coal mines are achieved". For the past few years, a number of sci-prone to coal and gas outbursts because of the com- entists have used this catastrophe theory to studyplexity of geologic conditions, large mining depth, problems of coal rock instability. Yin, Mou, Guo andhigh gas contents and low gas permeability. More Pan have respectively built beam and column modelsthan 50% of the state-owned coal mines are subject to and used the catastrophe theory to study the stabilitycoal-and gas-outbursts Gas disasters take place more problems of coal rocks". Bai, Shao, Zhong andfrequently in China than in any other part of the Miao have built beam and plate models and used thworld. The scale of the outbursts ranges from tens of catastrophe theory to study the mechanism of watertons to ten thousands of tons. Coal and gas outoutbursts at the top and bottom of coal tunnels-.bursts are complex disasters induced by mining proc- However, the catastrophe theory is rarely applied toesses. It is of theoretical and practical importancethe study of mechanism of coal and gas outbursts. Instudy the disaster mechanism so that the outbursts of our study, we built a thin plate model and used thegaseous coal rocks can be predicted, prevented and catastrophe theory to analyze the disaster mechanismcontrolled. For a long time, researchers across the of coal and gas outbursts of gaseous coal rocks andworld have carried out much important work to study have been able to provide a criterion of failure due tocoal and gas outbursts. However, outbursts still can- instabilitynot be predicted effectively because of their complexmechanism. When the catastrophe theory, established 2 Thin plate mechanical model of outburstby French mathematician R. Thom, is used in theoal rocksstudy of catastrophic phenomena, which are discon-tinuous and have unknown intrinsic deformationYu, Tan and Huang have carried out shock tubetestsand aae nnthurete and found that thegaseo中国煤化工 types of failurei.e. leCNMHGPressure outburstdoi:10.l06S1674-5264(00)60186sureased on the simulation tests of outburstsMining Science and TechnologyVol 20 No. 2Jiang found that layered shapes are formed in theother side gas under high pressure. Before the out-sidual coal rocks, where the layers are bounded by burst starts there is an emerging process for dangerdiscontinuous cracks. On the basis of these results, ous coal seams to move from deep under to the surZhao simplified the spalled coal rocks under gas face, regardless of whether the outburst occurs underpressure as circular and rectangular plate structures the condition of uncovering crosscuts or during roadand studied their stability problemsway tunneling. The spalled coal rock body can beIn mining practice, it is found that coal seams usu- approximately simplified as a thin plate model, asally occur between the hard roof and floor composed shown in Fig. 1. Assume that the rock plate has uni-of shale and sandstone. Generally, the roof and floorform thickness. Let the thickness of the plate be h, thechiefly block and restrict the outbursts during the out- length along the x axis a, the width along the y axis b,st process. In any mining process, at a certain dis- the in-plane loads Pr andhorizontal geostressahead of the mining face, stress concentration caused by deadweight of rock and rock formationly causes cracks in coal bodies. A certain the distribution intensity of the normal load q(in-ay accumulate within the cracks. cluding geostress and gas pressure)and the modulusWhen the tensile stress arising from gas pressure is of elasticity of the plate E. The upper and lower congreater than the tensile strength of the coal rocks, the straints of the bearing sides of the thin plate are re-cracks will be ripped and spalled bodies parallel to garded as simply supported constraints. The bucklingthe exposed surface will be formed. On one side of deformation of the thin plate under external forces ishe spalled body air is found in the tunnel and on the shown in Fig. lbHFig. I Thin plate mechanical model of coal rock bodyThe coal rock plate is buckled by tectonic stress. Its The work done by the normal load during the loadingdeflection can be expressed with a Double Fourier process is positive, soV=U-Pδ- gdedSin mrIn general, before any outburst takes place, thewhere Amwn is the amplitude of the mn-th term. The thickness t of the spalled coal rock is less than itsdeflection can be approximately expressed aswidth b(i.e, b/8srsb/5). This type of rock plate isregarded as a thin plate with a considerably largeA1(2) bending stiffness. Because its deflection is far lessthan its thickness, a bending theory of thin plate witha small deflection should be used in the analysis3 Catastrophe model of thin plate system With the deformation components Ez yyes yu omitted,of coal rocksthe deforming potential of the thin plate can be ex3.1 Potential function of the systenThe total potential of the thin plate system, V,canU=fJJ(o,6,+o, 6, +r,y, Xs, ds, dz (5)be expressed as a combination of the strain energy U where ds, ds, is an infinitesimally small element takenof the structure and the potential energy of the loadsfrom the deformed thin plate and ds and dsy are theV=U+P(3) lines中国煤化工 e curvatureCNMHGplawhere P, is a load acting on the structure; its corre- Pressed wiCyanosponding displacement and n the number of loadsLI Shugang et alCatastrophic mechanism of coal and gas outbursts and their prevention and controlabN.{1+axa2wdv22-1}-2N,waxThe stress components of the thin plate can be ex- Substituting the intemal forces into Eq (1 1) yieldspressed with the deflection equation asEz a2w awPEz(a2w.,I dxdy(12)Ez dwI+u dxdyThe work done by the normal load can be exSubstituting these strain and stress componentsinto the deformation potential expression and inte- W2grating z from -t/2 to t/2, the deformation potentialcan be expressed aslaba,(13)ds dsTherefore, the total potential of the system can(I-u)prd awaexpressed asa2 a2whereand the bending stiffness ofEWhen the deflection of the thin plate is very small,1 drdy(14)rections can be approximately expressed with thedeflection asTaking the Taylor expansion for the integral function of the above formula, truncating and then inte-grating, the approximate expression of the total po-tential function of the model system discussed can be(9) expressed asd9Pnab9Pπab5All the sides of the thin plate can be regarded asDIb abmply supported or clamped. Substituting Eq (9)intoPEq- (8)yields(15)U.d rd a'wa?w82叭ax2ayax中国煤化工The work done by the in-plane load during theto noaHCNMHGbuckling processMining Science and TechnologyVol 20 No. 2Only when the in-plane load P and normal load3Drt'ab(19P r'ab 9Pr x(16)meet this condition can the structure be stable andb2change from one equilibrium state to another equilibrium state. By Eq (22), we can depict the bifurcationset, as shown in Fig. 2.3Dn°ab(l1).9Pn2ab.9Pπab128b6Db_- I'aEBaba3DablIa26/+9P,rabFig. 2 Bifurcation set128a°128b°As can beseen from Fig. 2,the control space(18) which is composed of the in-plane load P and theThen the expression of the total system potentialnormal load q, is divided into 5 sections by the bifurcation set B. These sections are the point Qcan be simplified as a cusp catastrophe model with a branches B, and B2 of curve B, region E and region.and b as the control variables and x as the state van- They correspond to the different system states. Fromable. The variable a corresponds to the in-plane force the division of the control space by the bifurcation set,Pr and Py, the variable b to the normal force g and thewe can see that the gradual change of the in-planevariable x to the deflection An at the center of the load and normal uniformly distributed load, as con-trol variables, can cause abrupt state change. The(19)moving paths of point(P, q)in the control space havean obvious impact on the stability of coal rock. Thephase space is a three-dimensionmoving paths are very complex; two of them areed by the state variable x and the two controlschematically shown in Fig 3.variables a and b. The equation for the equilibriumsurface M isv=xtuxtyThe equation for the bifurcation set is4n3+27v2=021)3.3 Dynamic instability conditions of thin plateof coal rocksIn coal mining engineering, it is found that as min-Fig. 3 Moving paths of point (P, q) in control space anding depth increases, the likelihood of instability ofcoal rocks increases and the geostress in each direction tends to be equal. Under such conditions weNow we shall briefly discuss the stability changesassume P and Py are approximately equal Hence, we of a thin plate based on the division of the bifurcationlet P=PrPy Substituting P for Pr and P, in Eqs.(17)setand(18)and combining Eq (21), we can find a pointPoint Q corresponds to the smallest value of(P, q)of the bifurcation set in the control space(P, g) plane stress that causes the coal rock to be unstablethat meets the following condition:At this point, q is equal to O. Substituting 0 for g inEq (22)yieldsTP/b ahabla=0(22)3Dtab(11). 9Pi'(b.aH中国煤化工(23)CNMHG by catastrophetheory, is the same as the critical stress expression ofplate instability in the theory of plate and shellLI Shugang et alCatastrophic mechanism of coal and gas outbursts and their213The equilibrium equation corresponding to the two mining processes of exposed spalled coal rock underbranches B, and B, of curve B in2 has one single action of geostress and gas pressure, a simply sup.root and a pair of multiple roots. These roots corre- ported thin plate model is used and a method of caspond to one minimum value and one curve point of tastrophe theory is used to establish a cusp catastro-than Po. The point on the equilibrium surface corre- due to catastrophic change, has been provided la forthe potential function. At this time, the normal load g phe model of the system. An evaluation formula foris not equal to 0 and the in-plane load P is greater determining the instability of a thin plate of coal rock,sponding to(P, q)will jump suddenly2)The occurrence of coal and rock outbursts deThe equilibrium equation corresponding to region pends not only on the physical properties and dimenE in Fig. 2 has only one real root, which causes the sions of the exposed spalled coal rock, but also on thepotential function to have only one minimum value. magnitudes and changing paths of the in-plane andPoints on the equilibrium surfacese a stable normal loads. When the changes of the in-plane loadquilibrium in the system will notsuddenly. and the normal load are outside the bifurcation set,The in-plane load P may be lessqual to or the stability of the system does not change naturallygreater than PoWhen the changes of the in-plane and the normalThe equilibrium equation corresponding to region loads span the bifurcation set a slight disturbance ofin Fig. 2 has three different real roots, which causes the normal load causes catastrophic change of thethe potential function to have two minimum values state of the spalled coal rock.the system to be in a state of stable equilibrium, while effectively prevented enand one maximum value. There are three points on3)When the gas in the coal body is pre-drainedthe equilibrium surface corresponding to region J. the gas pressure is reduced and the normal load g isThe two points on the upper and lower leaves cause lowered. Thus, the coal and rock outbursts can bethe point on the middle leaf causes the system to be inan unstable equilibrium state. Theoretically, the point Acknowledgementson the middle leaf cannot be reached. For the point (P,g) to be in region J, the in-plane load must be greater Financial support for this work, provided by thethan Po.National Natural Science Foundation of ChinaThe curve m in Fig. 3 indicates that when theNos.50574072,50874089and50534049) and thechanges of the in-plane load P and normal load q are Special Scientific Foundation of the Shaanxi Departoutside the bifurcation set and the control variable(pment of Education(No. 08JK366)is gratefully acq)does not span the bifurcation set, the stability of knowledgedhe system does not change naturally. The changemakes the thin plate transit smoothly from one stableReferencesequilibrium state to another stable equilibrium statend catastrophic change does not occur. 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