Damage statistical mechanics model of top coal in steep top caving coal

Journal of University of Science and Technology BeijingVolume 10, Number 1, February 2003, Page 12MineralDamage statistical mechanics model of top coal in steep top caving coalPingwu Shi", Xingping Lai), and Zhaoning gao1)School of Enengy, Xi'an University of Science Technology, Xi'an 710054, China2)Dept of Resources Exploration & Management Engineering, Anhui University Science and Technology, Huainan 232001, China( Received2002-04-19)Abstract: Damageal mechanics model of horizontal section height in the top caving was constructed in the paper. The influencefactors including supporting pressure, dip angle and characteristic of coal on horizontal section height were analyzed as well. By termsof the practice project analysis, the horizontal section height increases with the increase of dip angle B and thickness of coal seam M. Dipangle of coal seam B has tremendous impact on horizontal section height, while thickness of coal seam M has slight impact. Whenthickness of coal seam is below 10 m, horizontal section height increases sharply. While thickness exceeds 15 m, it is not major factoifluencing on horizontal section height any longKey words: steep-grade coal; horizontal section height; damage; statistic mechanic modelTThis work was financially supported by the National Natural Science Fund of China(No.50274058).The value of horizontal section height in steep-grade ship can be described by the non-damage patterntop caving in China is usually 10m, with the maximum which Cauchy stress was simply replaced by the validvalue up to 16 m. It is a key question that the value is stress, namely, equivalent hypothesis of strain [3]. solitably chosen and optimized in the steep-grade coalthe damage constitutive relationship can be describedcaving. It is important for mining enterprise to improvethe horizontal section height possibly, so that excava- [o]=[o][-D]= [EIElLl-DIting ratio and moving frequency of working face can bedecreased and significant economic profits can be pro- where [ El is elastic matrix; [a] is strain matrix; [ Jisduced [1, 2damage matrix; [I is unit matrix; d] is stress matrix;lo]is valid stress matrix.It is proven that the process of forming unstable archconstruction in overlying rock strata is identical to the1.2 Construction of the damage evolution equationprocess of loading. When caused by the loading disA micro-unit is taken from the coal mass which isplacement exceeded the critical value, the coal masspposed to be linear. But it has non-linear characterwill be damaged. In the process, the top coal is pseudo- macro mechanic of state. Considering the homogeneitycontinuous medium between continuous medium and of internal construction. strength of each unit is notloose medium, which is complied with the macro dam- equal, and the damage is discontinuous in the processage mechanical characteristics. Accordingly, supportof loading. Based on the quoting statistical theoryng pressure, dip angle and coal mass features are taken postulated that every unit is accorded withinto consideration while optimizing horizontal section Weibull's distribution, the probability density functionheight based on the damage mechanic theorctorsis[4]influencing on horizontal section height in steep-gradetop caving are analyzed and reliable and efficient the()e-(」oretical evidences are presentedThere F is random distributional variant of micro-unit1 The construction of damage statistical m and Fo are Weibull's distributional parameters whichmechanic evolution modeldonate the mechanical characteristics of coal mass it is1.1 Construction of the damage constitutive equa-中国煤化工 resulting inCNMHGBased on the damage mechanic theory, in the condi-Under the external force. the constitutive relationCorrespondingauthorPingwusHiE-mail:xptest@sina.comPw. Shi et al, Damage statistical mechanics model of top coal in steep top caving coalion of isotropy damage, damage variant D can be symith the advancing of mining stress in coal massbolized with damage area and non-damage area of ma- transits from three dimensions to two dimensions andterialtends to zero near working face, and supporting preD=A=(÷)exp-(÷sure is distributed along the trend direction shownfigure 1It is called the damage evolution formula in which Athe damage area and a is non -damage area1.3 Determination of random distributional variantBecause coal-rock is subject to not only uniaxialstrain but also to stress and strain relationship so random distributional variant is expressed by parameter Fdetermined by Mohr-Coulomb criterion [5], that is=o,=astana+2ccospa=45°多where p is internal frictional angle, c is cohesionWhile, micro-units are damaged which illuminates Figure 1 Distribution of supporting pressure along the trendthat a donates the criticality of micro-units. It is inddirectioneated that top coal damage mining in steep-grade coalseam was stemmed from compressing and sheaAssuming 0,=On and 0, =03, according to refedamage. It is feasible to determine random distribu- [7, 8, through deducing, it can be expressed as beltional variant with mohr -Coulomb criterion as shown01=0,=Q=c.cotop-tan'aeman dcosBin equation(5)AQ=Ac- -tan'aeF=Fa=0,=astana+业where A is side pressure coefficient, M is thickness ofcoal seam, f is frictional coefficient between layers2 Breaking mechanics of top coalUSing Hoke rule, it can be gottenDeformation and damage of top coal are a compli2=(--0)=E(0-0)cated process, which is related to the burying conditions and mechanical characters of the coal-rock. How03=E8+Hotever, It depends on mining pressure in great extent. To Based on the equations(1),(3),(4),(5). (9), it can be got-educe the pressure, manual exploding and hydraulic tenweakening occasionally are required. In terms of the-ory and practice, it has been proven that coal seam minastana+ing resulted in redistribution of stress in the coal mass0=B(l-D)+10=Eexespecially in supporting pressure area where microcrack occurred and evolved, then, top coal tended to bedamaged. Transition from in-situ stress to supporting Based on the equations(6), (8),(10), it can be gottenpressure is a process of increment of strain step by stepMany experiments of synthesized caving illuminatethat vertical displacement evolved in exponential funEar'sin Bexp((Ac-cotpewiamatan'acosB+2)tion Given horizontal section height h, trend angle B ofcoal seam, strain along the trend direction isAc· cotceManatan'acosBinBProject analysis. Wnal mine is thewhere x is distance between maximum pressure posicoal base in中国煤化工 nous regiontion and working face. a and b are two constantsCN MH Gh trend anglebigger than 45. Horizontal section caving is the methodJ. Univ. Sci. Technol. Beijing, Vol 10, No 1, Feb 2003n special thick coal seam mining developed in recent section height increases sharply. While thickness ex10 years. Taking Liudaowan coal mine as example, the ceeds 15 m, it is not major factor influencing on hor-parameters of coal seam are shown as follows: a=0.01; izontal section height any long. By far, those do nob=2; E=10.7x10 MPa;x=2 m; f=0. 25; u=0. 2; take support pressure and dip angle and character ofp=30, A=0.54: Fo=11. 4 MPa; B=70%,c=3.7 MPa; coal seam into account, the conclusion is partial andM=35m.ImpracticalTaking parameters into equation (11), the horizontal 4 Conclusionsection height equals 7.7 m(h=7. 7m). The real maxi-mum height of top coal is 10 m[9]. It is practical to de-(1) The forming and unstable process of arch structermine the horizontal section height with equation ture in overlying coal rock is consistent with the pro(11)cess of loading. Moreover top coal complies with themacro damage mechanical characteristics3 Analysis of factors influencing on horizontal section(2)Because of mining influence, stress distributionin coal mass transits from three dimensional statesAccording to equation (11), the relationship curvestwo dimensional states and tends to be zero near thebetween h and B, M, c, x as shown in figures 2(a),working face(b),(c),(d),and(e).() Micro-unit strength of coal mass complies withWhen maximum supporting pressure is far awayfrom working face, horizontal section height tends to compressing and shearing, and it's random distributionncrease.When dip angle is lower than 60, horizontalvariant is accorded with the coulomb lawsection height does not exceed 10 m, while exceeding(4) Horizontal section height increases with the in-70, it could be elevated more than 20 m. When cohe- crement of dip angle B and thickness of coal seam Msion c and frictional angle increases, horizontal section Dip angle of coal seam B has tremendous impact onheight decreases significantly. When >30or c>4.0 horizontal section height, while thickness of coal seamMPa, the damage accumulation tends to be smooth. If M has slight impact. When cohesive strength c and innothing is done to break coal, horizontal section height ternal frictional angle increases, horizontal sectionsubjected to clamping of top rock and bottom rock. So ends, the bigger horizontal section height is choseshould be below 10m. In thin coal seam, top coal is height decreases notably. The far support pressure exwhen thickness of coal seam is below 10m. horizontal120M/Figure 2 The relation1(d),c(e)中国煤化工。b0CNMHG2345678910C/MPaPw. Shi et al, Damage statistical mechanics model of top coal in steep top caving coalRterence[6] Meifeng Cai and Xingping Lai, Evaluation on stability ofstope structure based on nonlinear dynamics of coupling ar[1] Pingwu Shi, Xingping Lai, and Yongping Wu, Research ontificial neural network [, Journal of University of Sciencethe simulative experiment system and application to theand Technology Beijing, 9(2002), No I, P.damaged regularity in composite rock-mass roadway [1, [7] Weijun Wang, Chaojiong Hou, and Renqin Xiong, RationalJournal of University of Science and Technology Beijing(indetermination of sublevel height of top coal in steep seam[J]Chinese),24(2002),No.3,p.231Chinese Journal of rock mechanics and Engineering(in[2] Zhonghui Chen and Heping Xie, Damage mechanics analysisChinese),20(2001),No.3,p.355on the distribution of abutment pressure around a coal face [8] Zhongming Jin, Theory and Technology in Top-coal Caving[], Chinese journal of rock mechanics and engineering. 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