基于中厚板理论的深部崩落转充填隔离矿柱稳定性分析
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摘要
在金属矿山崩落转充填开采过程中,隔离矿柱作为浅部向深部延伸的衔接部分,其合理尺寸的留设对于实现矿山安全高效回采具有重要意义.针对内蒙古某铅锌矿深部崩落转充填开采这一实际情况,对水平隔离矿柱建立了厚板力学模型.考虑到连续板联结处的弯矩不可忽略,基于中厚板理论推导得出了对边简支对边固支条件下的应力表达式.采用前处理软件HyperMesh构建矿区高精度六面体网格模型,并将矿区三维地质模型导入有限差分软件FLAC~(3D)之中,以705中段及上部围岩塑性区体积为依据近似得出作用在隔离矿柱之上的均布荷载,并应用最大拉应力理论计算出隔离矿柱安全厚度为20 m.利用数值模拟软件分析了所留水平隔离矿柱的力学行为及其稳定性.结果表明:隔离矿柱沉降值与塑性区均控制在容许范围之内,稳定性良好,验证了所留隔离矿柱厚度的合理性.
In the process of mining from caving to filling method in metal mines, it is significant to reserve reasonable size of insulating pillar, being considered as a connecting part from shallow to deep excavation, so as to realize safe and efficient mining. According to the field engineering condition of a lead zinc mine in Inner Mongolia, the thick plate mechanical model was established for the horizontal insulating pillar. Considering the fact that the moment at the support of the continuous plate cannot be neglected, a stress expression where the boundary condition of clamped along two sides and simply supported along other two sides was deduced based on the refined plate theory. The 3 D geological model was established by the pre-processing software HyperMesh accurately, in which all the elements were hexagonal rather than quadrangular. Then the model was imported to a commercial code named FLAC~(3 D). The uniformly distributed load acting on the insulating pillar was calculated and successfully applied in the model on basis of the plastic zone volume of surrounding rock above 705 level, and the thickness of the insulating pillar was calculated to be 20 m according to the maximum tensile stress theory. Finally, the mechanical behavior and stability of the designed insulating pillar was numerically analyzed. Numerical results indicate that the settlement value and plastic zone of the insulating pillar were controlled within allowable range due to the favorable stability, which validate the rationality of the designed thickness of reserved insulating pillar.
In the process of mining from caving to filling method in metal mines, it is significant to reserve reasonable size of insulating pillar, being considered as a connecting part from shallow to deep excavation, so as to realize safe and efficient mining. According to the field engineering condition of a lead zinc mine in Inner Mongolia, the thick plate mechanical model was established for the horizontal insulating pillar. Considering the fact that the moment at the support of the continuous plate cannot be neglected, a stress expression where the boundary condition of clamped along two sides and simply supported along other two sides was deduced based on the refined plate theory. The 3 D geological model was established by the pre-processing software HyperMesh accurately, in which all the elements were hexagonal rather than quadrangular. Then the model was imported to a commercial code named FLAC~(3 D). The uniformly distributed load acting on the insulating pillar was calculated and successfully applied in the model on basis of the plastic zone volume of surrounding rock above 705 level, and the thickness of the insulating pillar was calculated to be 20 m according to the maximum tensile stress theory. Finally, the mechanical behavior and stability of the designed insulating pillar was numerically analyzed. Numerical results indicate that the settlement value and plastic zone of the insulating pillar were controlled within allowable range due to the favorable stability, which validate the rationality of the designed thickness of reserved insulating pillar.
引文
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[12] BURGESS A S.Elastic analysis of soil-foundation interaction[J].Canadian Journal of Civil Engineering,1983,10(1):71-71.
[13] HUANG M H,THAMBIRATNAM D P.Analysis of plate resting on elastic supports and elastic foundation by finite strip method[J].Computers & Structures,2001,79(29/30):2547-2557.
[14] 谢洪阳,龚文惠,周大华,等.移动荷载作用下Winkler地基板的等参元分析[J].岩土力学,2007,28(7):1495-1500.XIE Hongyang,GONG Wenhui,ZHOU Dahua,et al.Analysis of elastic plate resting on Winkler foundation subjected to moving load by isoparametric element method[J].Rock and Soil Mechanics,2007,28(7):1495-1500.
[15] 贺广零.基于厚板理论的水平煤层顶板临界厚度的分析[J].地下空间与工程学报,2009,5(4):659-663.HE Guangling.Determination of critical thickness of stiff roof in coal mine based on thick plate theory[J].Chinese Journal of Underground Space & Engineering,2009,5(4):659-663.
[16] 李宝富,李小军,任永康.采场上覆巨厚砾岩层运动对冲击地压诱因的实验与理论研究[J].煤炭学报,2014,39(增1):31-37.LI Baofu,LI Xiaojun,REN Yongkang.Experimental and theoretical study on rock burst inducement by movement of superthick conglemerrate strata overlying working face[J].Journal of China Coal Society,2014,39(Sup 1):31-37.
[17] 彭康.海下金属矿床开采参数优化与安全预警研究[D].长沙:中南大学,2014:38-39.PENG Kang.Parameter optimization and safety early warning research related to exploitation of undersea metallic ores[D].Changsha:Central South University,2014:38-39.
[18] MINDLIN R D.Influence of rotary inertia and shear on flexural motions of isotropic,elastic plates[J].J Appl Mech,1951,18(1):31-38.
[19] 胡海昌.弹性力学的变分原理及其应用[M].北京:科学出版社,1981:470-471.HU Haichang.Variational principles of theory of elasticity with applications[M].Beijing:Science Press,1981:470-471.
[20] 铁摩辛柯 S,沃诺斯基 S.板壳理论[M].《板壳理论》翻译组,译.北京:科学出版社,1977:194-195.TIMOSHENKO S P.Theory of plate and shell[M].Theory of plate and shell translation team,translated.Beijing:Science Press,1977:194-195.
[21] 彭S S.煤矿地层控制[M].高博彦,韩持,译.北京:煤炭工业出版社,1984:136-140.PENG S S.Coal mine ground control[M].GAO Boyan,HAN Chi,translated.Beijing:China Coal Industry Publishing House,1984:136-140.
[22] 丁原辰.矿区地应力状态的声发射粗估法及其应用[J].煤炭工程师,1992,19(4):50-56.DING Yuanchen.Rock stress measurement by the AE method and its application to mine[J].Coal Engineer,1992,19(4):50-56.
[23] 朱和玲,周科平,肖雄,等.基于开采环境再造顶板最小安全厚度研究[J].矿冶工程,2008,28(1):13-17.ZHU Heling,ZHOU Keping,XIAO Xiong,et al.Study on the minimum safety thickness of artificial roof based on reconstructing mining environment[J].Mining and Metallurgical Engineering,2008,28(1):13-17.
[24] HOEK E,BROWN E.Practical estimates of rock mass strength[J].International Journal of Rock Mechanics and Mining Sciences,1997,34(8):1165-1186.
[25] 姜福兴.薄板力学解在坚硬顶板采场的适用范围[J].西安科技大学学报,1991,11(2):12-19.JIANG Fuxing.Application range of thin plate mechanics solution in hard roof and workface[J].Journal of Xi’an University of Science and Technology,1991,11(2):12-19.
[26] WANG C M,LIM G T,REDDY J N,et al.Relationships between bending solutions of Reissner and Mindlin plate theories[J].Engineering Structures,2001,23(7):838-849.
[2] 赵国彦,吴浩,陈英,等.矿山充填材料承载机制及压缩特性实验研究[J].中国矿业大学学报,2017,46(6):1251-1258.ZHAO Guoyan,WU Hao,CHEN Ying,et al.Experimental study on load-bearing mechanism and compaction characteristics of mine filling materials[J].Journal of China University of Mining & Technology,2017,46(6):1251-1258.
[3] 曹帅,宋卫东,薛改利,等.分层尾砂胶结充填体力学特性变化规律及破坏模式[J].中国矿业大学学报,2016,45(4):717-722.CAO Shuai,SONG Weidong,XUE Gaili,et al.Mechanical characteristics variation of stratified cemented tailing backfilling and its failure modes[J].Journal of China University of Mining & Technology,2016,45(4):717-722.
[4] 赵兴东.谦比希矿深部开采隔离矿柱稳定性分析[J].岩石力学与工程学报,2010,29(增):2616-2622.ZHAO Xingdong.Stability analysis of insulating pillar of excavation of chambishi copper mine in depth[J].Chinese Journal of Rock Mechanics & Engineering,2010,29(Sup):2616-2622.
[5] 徐恒,王贻明,吴爱祥,等.基于尖点突变理论的充填体下采空区安全顶板厚度计算模型[J].岩石力学与工程学报,2017,36(3):579-586.XU Heng,WANG Yiming,WU Aixiang,et al.A computational model of safe thickness of roof under filling body based on cusp catastrophe theory[J].Chinese Journal of Rock Mechanics & Engineering,2017,36(3):579-586.
[6] 杨敬轩,鲁岩,刘长友,等.拉压模量不同的多层顶板承载与破坏机理分析[J].中国矿业大学学报,2015,44(1):16-23.YANG Jingxuan,LU Yan,LIU Changyou,et al.Load bearing and failure mechanism of the multilayer roof with different tension and compression modulus[J].Journal of China University of Mining & Technology,2015,44(1):16-23.
[7] 徐曾和,徐小荷,唐春安.坚硬顶板下煤柱岩爆的尖点突变理论分析[J].煤炭学报,1995,20(5):485-491.XU Zenghe,XU Xiaohe,TANG Chunan.Theoretical analysis of a cusp catastrophe bump of coal pillar under hard rocks[J].Journal of China Coal Society,1995,20(5):485-491.
[8] 史红,姜福兴.采场上覆大厚度坚硬岩层破断规律的力学分析[J].岩石力学与工程学报,2004,23(18):3066-3069.SHI Hong,JIANG Fuxing.Mechanical analysis of rupture regularity of hard and massive overlying strata of longwall face[J].Chinese Journal of Rock Mechanics & Engineering,2004,23(18):3066-3069.
[9] 王新丰,高明中.变长工作面采场顶板破断机理的力学模型分析[J].中国矿业大学学报,2015,44(1):36-45.WANG Xinfeng,GAO Mingzhong.Mechanical model of fracture mechanism of stope roof for working face with variable length[J].Journal of China University of Mining & Technology,2015,44(1):36-45.
[10] 徐芝纶.弹性力学(下册):第4版[M].高等教育出版社,2006:1-2.XU Zhilun.Elastic mechanics (Volume 2 of 2):Fourth Edition[M].Beijing:Higher Education Press,2006:1-2.
[11] 钟阳,陈静云,王松岩.四边任意支承条件下弹性矩形厚板辛几何法解析解[J].大连理工大学学报,2005,45(5):717-722.ZHONG Yang,CHEN Jingyun,WANG Songyan.Theoretical solution for rectangular thick plate with arbitrary boundary conditions by symplectic geometry method[J].Journal of Dalian University of Technology,2005,45(5):717-722.
[12] BURGESS A S.Elastic analysis of soil-foundation interaction[J].Canadian Journal of Civil Engineering,1983,10(1):71-71.
[13] HUANG M H,THAMBIRATNAM D P.Analysis of plate resting on elastic supports and elastic foundation by finite strip method[J].Computers & Structures,2001,79(29/30):2547-2557.
[14] 谢洪阳,龚文惠,周大华,等.移动荷载作用下Winkler地基板的等参元分析[J].岩土力学,2007,28(7):1495-1500.XIE Hongyang,GONG Wenhui,ZHOU Dahua,et al.Analysis of elastic plate resting on Winkler foundation subjected to moving load by isoparametric element method[J].Rock and Soil Mechanics,2007,28(7):1495-1500.
[15] 贺广零.基于厚板理论的水平煤层顶板临界厚度的分析[J].地下空间与工程学报,2009,5(4):659-663.HE Guangling.Determination of critical thickness of stiff roof in coal mine based on thick plate theory[J].Chinese Journal of Underground Space & Engineering,2009,5(4):659-663.
[16] 李宝富,李小军,任永康.采场上覆巨厚砾岩层运动对冲击地压诱因的实验与理论研究[J].煤炭学报,2014,39(增1):31-37.LI Baofu,LI Xiaojun,REN Yongkang.Experimental and theoretical study on rock burst inducement by movement of superthick conglemerrate strata overlying working face[J].Journal of China Coal Society,2014,39(Sup 1):31-37.
[17] 彭康.海下金属矿床开采参数优化与安全预警研究[D].长沙:中南大学,2014:38-39.PENG Kang.Parameter optimization and safety early warning research related to exploitation of undersea metallic ores[D].Changsha:Central South University,2014:38-39.
[18] MINDLIN R D.Influence of rotary inertia and shear on flexural motions of isotropic,elastic plates[J].J Appl Mech,1951,18(1):31-38.
[19] 胡海昌.弹性力学的变分原理及其应用[M].北京:科学出版社,1981:470-471.HU Haichang.Variational principles of theory of elasticity with applications[M].Beijing:Science Press,1981:470-471.
[20] 铁摩辛柯 S,沃诺斯基 S.板壳理论[M].《板壳理论》翻译组,译.北京:科学出版社,1977:194-195.TIMOSHENKO S P.Theory of plate and shell[M].Theory of plate and shell translation team,translated.Beijing:Science Press,1977:194-195.
[21] 彭S S.煤矿地层控制[M].高博彦,韩持,译.北京:煤炭工业出版社,1984:136-140.PENG S S.Coal mine ground control[M].GAO Boyan,HAN Chi,translated.Beijing:China Coal Industry Publishing House,1984:136-140.
[22] 丁原辰.矿区地应力状态的声发射粗估法及其应用[J].煤炭工程师,1992,19(4):50-56.DING Yuanchen.Rock stress measurement by the AE method and its application to mine[J].Coal Engineer,1992,19(4):50-56.
[23] 朱和玲,周科平,肖雄,等.基于开采环境再造顶板最小安全厚度研究[J].矿冶工程,2008,28(1):13-17.ZHU Heling,ZHOU Keping,XIAO Xiong,et al.Study on the minimum safety thickness of artificial roof based on reconstructing mining environment[J].Mining and Metallurgical Engineering,2008,28(1):13-17.
[24] HOEK E,BROWN E.Practical estimates of rock mass strength[J].International Journal of Rock Mechanics and Mining Sciences,1997,34(8):1165-1186.
[25] 姜福兴.薄板力学解在坚硬顶板采场的适用范围[J].西安科技大学学报,1991,11(2):12-19.JIANG Fuxing.Application range of thin plate mechanics solution in hard roof and workface[J].Journal of Xi’an University of Science and Technology,1991,11(2):12-19.
[26] WANG C M,LIM G T,REDDY J N,et al.Relationships between bending solutions of Reissner and Mindlin plate theories[J].Engineering Structures,2001,23(7):838-849.
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