石膏矿老采空区塑性支撑系统的突变失稳分析
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摘要
采空区支撑系统稳定性研究是保证石膏矿区安全生产的关键,为此构建塑性区的矿柱–岩梁支撑系统,将岩梁和矿柱分别视为能量释放体和能量耗散体,并运用能量理论构建支撑系统尖点突变模型,得出支撑体系相关的失稳判别条件。研究结果表明:支撑系统失稳是能量释放、耗散与支撑系统变形不协调的结果,当α>0时,系统能量释放与系统变形协调,支撑系统按路径I由下叶稳态渐进过度到上叶稳态的准静态过程;当α<0时,由于能量释放与系统变形不能协调,系统会按路径II由下叶稳态突跳到上叶稳态的突变过程,此过程使得多余的能量释放致使支撑系统发生动力学失稳问题。而后对支撑系统几何参数的敏感度进行分析,得出影响因素敏感度大小顺序为:顶板厚度>塑性区宽度>矿房跨度>矿柱宽度>矿柱高度矿。结合工程实例,根据各区开采几何参数不同对采空区进行分类,并运用突变理论对各类采空区支撑系统稳定性进行分析,得出D类区域为危险采区,与现场调研结果一致。
The stability of the goaf support system is the key to safe production in gypsum mines. A pillar-beam support system in plastic zones was constructed,and the beam and pillar were taken as the energy releaser and energy dissipater respectively. A cusp catastrophe model was established based on the energy theory,and the condition of instability of the support system was obtained. The results indicate that the instability of support system is caused by the incompatibility of energy release,energy dissipation and geometric deformation. When α>0,the energy released from the support system is compatible with the geometric deformation. The support system experiences a quasi-static process from the static state in the bottom leaf to the static state in the top leaf along Path I. When α<0,the energy released from the support system cannot be in tune with the geometric deformation. The support system experiences a catastrophic process along Path II. The evolution from the static state in the bottom leaf to the static state in the top leaf is not progressive,but catastrophic. The redundant energy released in this process leads to the mechanical instability of the support system. The sensitivity of the geometric parameters of the support system was analyzed as well. These parameters are ranked according to their sensitivity from high to low,as is shown below:beam thickness>plastic zone width>room span>pillar width>pillar height. Based on the actual engineering examples,the goaf was classified according to the geometric parameters. The energy catastrophe theory was applied to analyze the stability of support system of goaf in different classes. The analysis results showed that class D goaf should be labeled as the unstable zone,which was consistent with the result of field research. The energy catastrophe theory is thus shown to demonstrate the non-linear mechanical mechanism of support system instability in room-pillar mining goaf.
The stability of the goaf support system is the key to safe production in gypsum mines. A pillar-beam support system in plastic zones was constructed,and the beam and pillar were taken as the energy releaser and energy dissipater respectively. A cusp catastrophe model was established based on the energy theory,and the condition of instability of the support system was obtained. The results indicate that the instability of support system is caused by the incompatibility of energy release,energy dissipation and geometric deformation. When α>0,the energy released from the support system is compatible with the geometric deformation. The support system experiences a quasi-static process from the static state in the bottom leaf to the static state in the top leaf along Path I. When α<0,the energy released from the support system cannot be in tune with the geometric deformation. The support system experiences a catastrophic process along Path II. The evolution from the static state in the bottom leaf to the static state in the top leaf is not progressive,but catastrophic. The redundant energy released in this process leads to the mechanical instability of the support system. The sensitivity of the geometric parameters of the support system was analyzed as well. These parameters are ranked according to their sensitivity from high to low,as is shown below:beam thickness>plastic zone width>room span>pillar width>pillar height. Based on the actual engineering examples,the goaf was classified according to the geometric parameters. The energy catastrophe theory was applied to analyze the stability of support system of goaf in different classes. The analysis results showed that class D goaf should be labeled as the unstable zone,which was consistent with the result of field research. The energy catastrophe theory is thus shown to demonstrate the non-linear mechanical mechanism of support system instability in room-pillar mining goaf.
引文
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[18]曹胜根,曹洋,姜海军.块段式开采区段煤柱突变失稳机制研究[J].采矿与安全工程学报,2014,(6):907–913.(CAO Shenggen,CAO Yang,JIANG Haijun. Study on mechanism of sudden instabilityofblockcoalpillarinblockmining[J].JournalofMining and Safety Engineering,2014,(6):907–913.(in Chinese))
[19]郑东健,雷霆.对“基于突变理论的高拱坝失稳判据研究”讨论的答复[J].岩土工程学报,2012,34(5):968.(ZHENG Dongjian,LEI Ting. Reply to the discussion on “instability criterion of high arch dambasedoncatastrophetheory”[J].ChineseJournalofGeotechnical Engineering,2012,34(5):968.(in Chinese))
[20]祝云华,刘新荣,黄明,等.深埋隧道开挖围岩失稳突变模型研究[J].岩土力学,2009,30(3):805–809.(ZHUYunhua,LIU Xinrong,HUANGMing,etal.Studyoncatastrophicmodelof surroundingrockfailureindeeptunnelexcavation[J].RockandSoil Mechanics,2009,30(3):805–809.(in Chinese))
[21]王水林,郑宏,刘泉声,等.应变软化岩体分析原理及其应用[J].岩土力学,2014,35(3):609–622.(WANG Shuilin,ZHENG Hong,LIUQuansheng,etal.Analysisprincipleandapplicationofstrain softening rock mass[J]. Rock and Soil Mechanics,2014,35(3):609–622.(in Chinese))
[22]高明仕,窦林名,张农,等.煤(矿)柱失稳冲击破坏的突变模型及其应用[J].中国矿业大学学报,2005,34(4):433–437.(GAO Mingshi,DOULinming,ZHANGLong,etal.Cuspcatastrophic modelforinstabilityofcoalpillarburstdamageandanalysisofits application[J].JournalofChinaUniversityofMiningand Technology,2005,34(4):433–437.(in Chinese))
[23]周宗红,侯克鹏,任凤玉.分段空场崩落采矿法顶板稳定性分析[J].采矿与安全工程学报,2012,29(4):538–542.(ZHOU Zonghong,HOU Kepeng,REN Fengyu. Roof stability analysis of sublevel open stopeandcavingminingmethod[J].JournalofMiningandSafety Engineering,2012,29(4):538–542.(in Chinese))
[24]徐必根,黄英华,刘小林.护顶层对石膏矿采空区稳定性影响研究[J].矿业研究与开发,2007,27(5):20–22.(XUBigen,HUANG Yinghua,LIU Xiaolin. Influence of top-safeguarding layer on stability ofmined-outareaingypsummines[J].MiningResearchand Development,2007,27(5):20–22.(in Chinese))
[2]CAO Z Z,ZHOU Y J. Research on instability mechanism and type of ore pillar based on the fold catastrophe theory[J]. Computer Modeling in Engineering and Sciences,2017,113(2):275–293.
[3]CAOZZ,ZHOUYJ.Researchoncoalpillarwidthinroadway drivingalonggoafbasedonthestabilityofkeyblock[J].Computers Materials and Continua,2015,48(2):77–90.
[4]WATTIMENA R K,KRAMADIBRATA S,SIDI I D,et al. Developing coalpillarstabilitychartusinglogisticregression[J]International Journal of RockMechanicsandMining Sciences,2013,58(1):55–60.
[5]GHASEMI E,ATAEI M,SHAHRIAR K. An intelligent approach to predictpillarsizingindesigningroomandpillarcoalmines[J]International Journal of Rock Mechanics and Mining Sciences,2014,65(1):86–95.
[6]VERMACP,PORATHURJL,THOTENR,etal.Empirical approaches for design of web pillars in highwall mining:review and analysis[J]. Geotechnical and Geological Engineering,2014,32(2):587–599.
[7]HENLEYS.Catastrophetheorymodelsingeology[J].Mathematical Geology,1976,8(6):649–655.
[8]THOMR.Stabilitéstructurelleetmorphogénèse[M].NewYork:Benjamin,1972:1–60.
[9]潘岳,王志强.狭窄煤柱冲击地压的折迭突变模型[J].岩土力学,2004,25(1):23–30.(PAN Yue,WANG Zhiqiang. Fold catastrophe modelofrockburstinnarrowcoalpillar[J].RockandSoil Mechanics,2004,25(1):23–30.(in Chinese))
[10]夏开宗,陈从新,刘秀敏,等.基于突变理论的石膏矿矿柱–护顶层支撑系统的破坏分析[J].岩石力学与工程学报,2016,35(增2):3837–3845.(XIAKaizong,CHENCongxin,LIUXiumin,etal.Analysisofcatastrophetheoryofpillargypsummine-retaining top-levelsupportsystemfailure[J].ChineseJournalofRockMechanics and Engineering,2016,35(Supp.2):3 837–3 845.(in Chinese))
[11]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,(5):485–491.(XU Zenghe,XU Xiaohe,TANGChun′an.Theoreticalanalysisofacuspcatastrophebumpof coal pillar under hard rocks[J]. Journal of China Coal Society,1995,(5):485–491.(in Chinese))
[12]秦四清,王思敬.煤柱–顶板系统协同作用的脆性失稳与非线性演化机制[J].工程地质学报,2005,13(4):437–446.(QINSiqing,WANGSijing.Instabilityleadingtorockburstsandnonlinear evolutionarymechani-smsforcoal-pillar-and-roofsystem[J].Journal of Engineering Geology,2005,13(4):437–446.(in Chinese))
[13]王连国,宋扬,缪协兴.基于尖点突变模型的煤层底板突水预测研究[J].岩石力学与工程学报,2003,22(4):573–577.(WANG Lianguo,SONGYang, MIAOXiexing.Studyonpredictionof water-inrushfromcoalfloorbasedoncuspcatastrophicmodel[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(4):573–577.(in Chinese))
[14]张钦礼,曹小刚,王艳利,等.基于尖点突变模型的采场顶板——矿柱稳定性分析[J].中国安全科学学报,2011,21(10):52–57.(ZHANG Qinli,CAO Xiaogang,WANG Yanli,et al. Stability analysis of stope roof-pillar based on cusp catastrophe model[J]. China Safety Science Journal,2011,21(10):52–57.(in Chinese))
[15]郭文兵,邓喀中,邹友峰.条带煤柱的突变破坏失稳理论研究[J].中国矿业大学学报,2005,(1):80–84.(GUOWenbing,DENG Kezhong,ZOUYoufeng.Cuspcatastrophicmodelofinstabilityof strip coal pillar along strike[J]. Journal of China University of Mining and Technology,2005,(1):80–84.(in Chinese))
[16]李明,茅献彪,茅蓉蓉,等.基于尖点突变模型的巷道围岩屈曲失稳规律研究[J].采矿与安全工程学报,2014,(3):379–384.(LI Ming,MAOXianbiao,MAORongrong,etal.Studyonbuckling instabilityofsurroundingrockbasedoncuspcatastrophemodel[J].Journal of Mining and Safety Engineering,2014,(3):379–384.(in Chinese))
[17]谭毅,郭文兵,赵雁海.条带式开采煤柱系统突变失稳机制及工程稳定性研究[J].煤炭学报,2016,(7):1 667–1 674.(TAN Yi,GUOWenbing, ZHAOYanhai.Studyoncatastropheinstability mechanism and engineering stability of strip mining system[J]. Journal of Coal Industry,2016,(7):1 667–1 674.(in Chinese))
[18]曹胜根,曹洋,姜海军.块段式开采区段煤柱突变失稳机制研究[J].采矿与安全工程学报,2014,(6):907–913.(CAO Shenggen,CAO Yang,JIANG Haijun. Study on mechanism of sudden instabilityofblockcoalpillarinblockmining[J].JournalofMining and Safety Engineering,2014,(6):907–913.(in Chinese))
[19]郑东健,雷霆.对“基于突变理论的高拱坝失稳判据研究”讨论的答复[J].岩土工程学报,2012,34(5):968.(ZHENG Dongjian,LEI Ting. Reply to the discussion on “instability criterion of high arch dambasedoncatastrophetheory”[J].ChineseJournalofGeotechnical Engineering,2012,34(5):968.(in Chinese))
[20]祝云华,刘新荣,黄明,等.深埋隧道开挖围岩失稳突变模型研究[J].岩土力学,2009,30(3):805–809.(ZHUYunhua,LIU Xinrong,HUANGMing,etal.Studyoncatastrophicmodelof surroundingrockfailureindeeptunnelexcavation[J].RockandSoil Mechanics,2009,30(3):805–809.(in Chinese))
[21]王水林,郑宏,刘泉声,等.应变软化岩体分析原理及其应用[J].岩土力学,2014,35(3):609–622.(WANG Shuilin,ZHENG Hong,LIUQuansheng,etal.Analysisprincipleandapplicationofstrain softening rock mass[J]. Rock and Soil Mechanics,2014,35(3):609–622.(in Chinese))
[22]高明仕,窦林名,张农,等.煤(矿)柱失稳冲击破坏的突变模型及其应用[J].中国矿业大学学报,2005,34(4):433–437.(GAO Mingshi,DOULinming,ZHANGLong,etal.Cuspcatastrophic modelforinstabilityofcoalpillarburstdamageandanalysisofits application[J].JournalofChinaUniversityofMiningand Technology,2005,34(4):433–437.(in Chinese))
[23]周宗红,侯克鹏,任凤玉.分段空场崩落采矿法顶板稳定性分析[J].采矿与安全工程学报,2012,29(4):538–542.(ZHOU Zonghong,HOU Kepeng,REN Fengyu. Roof stability analysis of sublevel open stopeandcavingminingmethod[J].JournalofMiningandSafety Engineering,2012,29(4):538–542.(in Chinese))
[24]徐必根,黄英华,刘小林.护顶层对石膏矿采空区稳定性影响研究[J].矿业研究与开发,2007,27(5):20–22.(XUBigen,HUANG Yinghua,LIU Xiaolin. Influence of top-safeguarding layer on stability ofmined-outareaingypsummines[J].MiningResearchand Development,2007,27(5):20–22.(in Chinese))