采空区煤柱-顶板系统失稳的力学分析
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摘要
基于温克尔假设,突破把坚硬顶板视为弹性梁的传统思想,把坚硬顶板视为弹性板,将煤柱等效为连续均匀分布的支撑弹簧,从而形成煤柱-顶板相互作用系统;同时,将煤柱视为应变软化介质,采用近似的Weibull分布描述它的损伤本构模型,依据板壳理论和非线性动力学理论对采空区煤柱-顶板系统失稳机理进行了研究,得出了系统失稳的突变机制,并给出了系统失稳的数学判据和力学条件;最后,以马脊梁矿为工程实例进行分析。结果表明,理论分析值与工程实测数据吻合较好,为进一步研究煤柱-顶板相互作用系统和制定相关规范提供了重要参考。
Based on the Winkler's hypothesis,the stiff roof was assumed as an elastic beam.It was totally different with the conventional idea that the stiff roof was assumed as an elastic plate,and the coal pillars were equal to continuously and uniformly distributed support springs.Then,the coal pillar and roof interaction system was formed.It was also assumed that the coal pillar was a strain-softening medium,and the damage constitutive model could be described by the approximate Weibull's distribution.Authors presented the instability mechanism of coal pillar and roof interaction system by using the plate mechanics and the nonlinear dynamics theory,then,the catastrophe mechanism of the system instability was gotten and the mathematical criterion and mechanical condition were given.Finally,taking Majiliang coal mine as an engineering example,the results show that a good agreement exists between the theoretical analysis vaule and engineering real test data which provides an important reference for the further research of the coal pillar and roof interaction system and constitution of relevant codes.
Based on the Winkler's hypothesis,the stiff roof was assumed as an elastic beam.It was totally different with the conventional idea that the stiff roof was assumed as an elastic plate,and the coal pillars were equal to continuously and uniformly distributed support springs.Then,the coal pillar and roof interaction system was formed.It was also assumed that the coal pillar was a strain-softening medium,and the damage constitutive model could be described by the approximate Weibull's distribution.Authors presented the instability mechanism of coal pillar and roof interaction system by using the plate mechanics and the nonlinear dynamics theory,then,the catastrophe mechanism of the system instability was gotten and the mathematical criterion and mechanical condition were given.Finally,taking Majiliang coal mine as an engineering example,the results show that a good agreement exists between the theoretical analysis vaule and engineering real test data which provides an important reference for the further research of the coal pillar and roof interaction system and constitution of relevant codes.
引文
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[17]潘一山,章梦涛.用突变理论分析冲击矿压发生的物理过程[J].阜新矿业学院学报,1992,11(1):12-18.PAN Yi-shan,ZHANG Meng-tao.Analysis on thePhysical Process of Rock Bursts by Catastrophe The-ory[J].Journal of Fuxin Mining Institute,1992,11(1):12-18.
[18]QIN Si-qing,WANG Si-jing,LONG Hui,et al.A newApproach to Estimating Geo-stresses from Laborato-ry Kaiser Effect Measurement[J].International Jour-nal of Rock Mechanics and Mining Science,1999,36(8):1 073-1 077.
[19]仪垂祥.非线性科学及其在地学中的应用[M].北京:气象出版社,1995.YI Chui-xiang.Nonlinear Science and Its Applicationin Geotechnology[M].Beijing:China MeteorologicalPress,1995.
[20]宋永津.控制煤层坚硬难冒顶板技术[M].北京:煤炭工业出版社,2001.SONG Yong-jin.The Technology of Controlling CoalStiff Roof Difficult to Cave[M].Beijing:China CoalIndustry Publishing House,2001.
[2]章梦涛,徐曾和,潘一山.冲击地压和突出的统一失稳理论[J].煤炭学报,1991,16(4):48-53.ZHANG Meng-tao,XU Zeng-he,PAN Yi-shan.Uni-form Instability Theory for Rock Burst and Bump[J].Journal of China Coal Society,1991,16(4):48-53.
[3]潘岳.矿井断层冲击地压的折迭突变模型[J].岩石力学与工程学报,2001,20(1):43-48.PAN Yue.Fold Catastrophe Model of Mining FaultRock Burst[J].Chinese Journal of Rock Mechanicsand Engineering,2001,20(1):43-48.
[4]谭云亮.矿山岩层运动非线性动力学特征研究[D].沈阳:东北大学,1996.TAN Yun-liang.Research on the Nonlinear DynamicCharacteristic of Mining Overburden Movement[D].Shenyang:Northeast University,1996.
[5]尹光志,代高飞,万玲,等.岩石微裂纹演化的分岔混沌与自组织特征[J].岩石力学与工程学报,2002,21(5):635-639.YIN Guang-zhi,DAI Gao-fei,WAN Ling,et al.Char-acteristics of Bifurcation,Chaos and Self-organizationof Evolution of Micro-cracks in Rock[J].ChineseJournal of Rock Mechanics and Engineering,2002,21(5):635-639.
[6]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 Zeng-he,XU Xiao-he,TANG Chun-an.Analysisof a Cusp Catastrophe Bump of Coal Pillar UnderHard Rocks[J].Journal of China Coal Society,1995,20(5):485-491.
[7]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.QIN Si-qing,WANG Si-jing.Instability Leading toRockbursts and Nonlinear Evolutionary Mechanismsfor Coal-pillar-and-roof System[J].Journal of Engi-neering Geology,2005,13(4):437-446.
[8]俞茂宏,ODA Y,盛谦,等.统一强度理论的发展及其在土木水利等工程中的应用和经济意义[J].建筑科学与工程学报,2005,22(1):24-41.YU Mao-hong,ODA Y,SHENG Qian,et al.Develop-ment of Unified Strength Theory and Its Applicationsin Civil Engineering and Its Economic Significance[J].Journal of Architecture and Civil Engineering,2005,22(1):24-41.
[9]刘忠,沈蒲生,陈铖.惯性荷载和地震荷载作用下单桩横向非线性动力响应简化分析[J].中国公路学报,2005,18(3):66-69.LIU Zhong,SHEN Pu-sheng,CHEN Cheng.Simpli-fied Analysis for Lateral Nonlinear Dynamic Responseof Single Pile Under Inertial and Seismic Loads[J].China Journal of Highway and Transport,2005,18(3):66-69.
[10]赵明华,曾昭宇,刘晓明,等.考虑轴向横向荷载共同作用的基桩可靠度[J].建筑科学与工程学报,2005,22(2):57-60.ZHAO Ming-hua,ZENG Zhao-yu,LIU Xiao-ming,et al.Reliability of Pile Foundation Under Verticaland Lateral Loads[J].Journal of Architecture andCivil Engineering,2005,22(2):57-60.
[11]徐芝伦.弹性力学:下册[M].3版.北京:高等教育出版社,1992.XU Zhi-lun.Elasticity Mechanics:Volume 2[M].3rded.Beijing:Higher Education Press,1992.
[12]易伟建,杨随新.软土地基上的土-结构动力相互作用[J].建筑科学与工程学报,2005,22(2):61-65.YI Wei-jian,YANG Sui-xin.Soil-structure DynamicInteraction Based on Soft Soil Foundation[J].Journalof Architecture and Civil Engineering,2005,22(2):61-65.
[13]吴建营,李杰.混凝土弹塑性损伤本构关系统一模型[J].建筑科学与工程学报,2005,22(4):15-21.WU Jian-ying,LI Jie.Unified Elasto-plastic DamageConstitutive Relations Model for Concrete[J].Journalof Architecture and Civil Engineering,2005,22(4):15-21.
[14]钱鸣高,石平五.矿山压力与岩层控制[M].北京:中国矿业大学出版社,2003.QIAN Ming-gao,SHI Ping-wu.Mining Pressure andStrata Control[M].Beijing:China University Press ofMining and Technology,2003.
[15]派克R,根勃尔W L.钢筋混凝土板[M].上海:同济大学出版社,1992.PARK R,GAMBE W L.Reinforced Concrete Plate[M].Shanghai:Tongji University Press,1992.
[16]HUDSON J A,FAIRHURST C.Tensile Strength,Weibull s Theory and a General Statistical Approachto Rock Failure[C]//TEENI M.The Proceedings ofthe Southampton 1969 Civil Engineering MaterialsConference:Part 2.London:Wiley-interscience,1971.
[17]潘一山,章梦涛.用突变理论分析冲击矿压发生的物理过程[J].阜新矿业学院学报,1992,11(1):12-18.PAN Yi-shan,ZHANG Meng-tao.Analysis on thePhysical Process of Rock Bursts by Catastrophe The-ory[J].Journal of Fuxin Mining Institute,1992,11(1):12-18.
[18]QIN Si-qing,WANG Si-jing,LONG Hui,et al.A newApproach to Estimating Geo-stresses from Laborato-ry Kaiser Effect Measurement[J].International Jour-nal of Rock Mechanics and Mining Science,1999,36(8):1 073-1 077.
[19]仪垂祥.非线性科学及其在地学中的应用[M].北京:气象出版社,1995.YI Chui-xiang.Nonlinear Science and Its Applicationin Geotechnology[M].Beijing:China MeteorologicalPress,1995.
[20]宋永津.控制煤层坚硬难冒顶板技术[M].北京:煤炭工业出版社,2001.SONG Yong-jin.The Technology of Controlling CoalStiff Roof Difficult to Cave[M].Beijing:China CoalIndustry Publishing House,2001.
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