考虑两侧煤柱与弹性煤体基础的基本顶板初次破断特征
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摘要
建立考虑两侧煤柱支撑与实体煤作为弹性基础的基本顶板初次断裂力学模型,采用差分算法及主弯矩破断准则计算研究得到如下结论。(1)基本顶初始断裂位置为偏较弱煤柱侧悬顶区中部下表面(弹性基础系数k较小,基本顶厚度h、弹模E较大时),反之为偏较弱煤柱侧的长边实体煤区上表面;(2)两侧煤柱的宽度L1,L2及支撑系数km1,km2改变时,基本顶中部区与实体煤区的主弯矩及位置几乎不改变,而两侧煤柱区的主弯矩及位置变化显著;(3) E,h大,而L1,km1,L2,km2小时,基本顶在两侧煤柱区不断裂,破断顺序为:偏较弱煤柱侧的悬顶区中部下表面→偏较弱煤柱侧长边实体煤区上表面,断裂特征为非对称"=-X"型;反之基本顶在煤柱区会断裂,破断顺序为:偏较弱煤柱侧长边实体煤区上表面→偏较弱煤柱侧悬顶区中部下表面→较强煤柱区上表面→较弱煤柱区上表面,断裂特征为非对称"O-X"型;而L1,km1较小,L2,km2较大时,只较弱煤柱侧基本顶不破断,最终断裂形态为非对称"U-X"型;(4)比值k/E或k/(Eh3)不变(k,E,h改变时,km1及km2与k保持某个任意比值不变),基本顶破断规律不变。
The mechanical model of first fracturing of main roof considering the support of coal pillars and solid coal as elastic foundation on both sides of stope is established.Using the differential algorithm and the fracture criterion of primary moment,it is found that(1) when the elastic foundation coefficient k is smaller as well as the thickness of main roof h and the elastic modulus E is larger,the initial fracture position of main roof is the lower surface of central region of hanging roof area on weaker coal pillar side.On the contrary,the position is the upper surface of long side area ahead of solid coal on weaker coal pillar side.(2) When the support coefficients km1,km2 and the widths L1,L2 of coal pillars on the two sides of stope change,the primary moments and their positions ahead of coal wall in the central area of main roof and solid coal area are almost unchanged.However,the values and the positions of primary moments of main roof in coal pillars area on the two sides of stope change significantly.(3) When the thickness h and elastic modulus E of main roof are larger and the values of L1,km1,L2 and km2 are smaller,the main roof in coal pillars area on the twosides of stope will not fracture.So the fracturing order of the roof is that the lower surface of central region of hanging roof area on weaker coal pillar side → the upper surface of long-side solid coal area on weaker coal pillar side,and the final fracture form is the type of asymmetric"=-X".On the contrary,the main roof in coal pillars area on the two sides of stope will fracture.Thus the fracturing order is that the upper surface of long-side solid coal area on weaker coal pillar side → the lower surface of central region of hanging roof area on weaker coal pillar side → the upper surface of coal pillar area on stronger coal pillar side → the upper surface of coal pillar area on weaker coal pillar side,and the final fracture form is the type of asymmetric "O-X".However,when L1,km1 are smaller and L2,km2 are larger,only on weaker coal pillar side,the main roof will not fracture,and the final fracture form is the type of asymmetric "U-X".(4) When k,E and h change as well as km1 and km2 keep a certain arbitrary ratio constant with k,the ratio k/E or k/(Eh~3) is unchangeable and the fracture law of main roof is invariant.
The mechanical model of first fracturing of main roof considering the support of coal pillars and solid coal as elastic foundation on both sides of stope is established.Using the differential algorithm and the fracture criterion of primary moment,it is found that(1) when the elastic foundation coefficient k is smaller as well as the thickness of main roof h and the elastic modulus E is larger,the initial fracture position of main roof is the lower surface of central region of hanging roof area on weaker coal pillar side.On the contrary,the position is the upper surface of long side area ahead of solid coal on weaker coal pillar side.(2) When the support coefficients km1,km2 and the widths L1,L2 of coal pillars on the two sides of stope change,the primary moments and their positions ahead of coal wall in the central area of main roof and solid coal area are almost unchanged.However,the values and the positions of primary moments of main roof in coal pillars area on the two sides of stope change significantly.(3) When the thickness h and elastic modulus E of main roof are larger and the values of L1,km1,L2 and km2 are smaller,the main roof in coal pillars area on the twosides of stope will not fracture.So the fracturing order of the roof is that the lower surface of central region of hanging roof area on weaker coal pillar side → the upper surface of long-side solid coal area on weaker coal pillar side,and the final fracture form is the type of asymmetric"=-X".On the contrary,the main roof in coal pillars area on the two sides of stope will fracture.Thus the fracturing order is that the upper surface of long-side solid coal area on weaker coal pillar side → the lower surface of central region of hanging roof area on weaker coal pillar side → the upper surface of coal pillar area on stronger coal pillar side → the upper surface of coal pillar area on weaker coal pillar side,and the final fracture form is the type of asymmetric "O-X".However,when L1,km1 are smaller and L2,km2 are larger,only on weaker coal pillar side,the main roof will not fracture,and the final fracture form is the type of asymmetric "U-X".(4) When k,E and h change as well as km1 and km2 keep a certain arbitrary ratio constant with k,the ratio k/E or k/(Eh~3) is unchangeable and the fracture law of main roof is invariant.
引文
[1]钱鸣高,石平五,许家林.矿山压力与岩层控制[M].徐州:中国矿业大学出版社,2010:73-84,93-99,198,221-224.
[2] KE Yang,HE Xiang,DOU Litong,et al.Experimental investigation into stress-relief characteristics with upward large height and upward mining under hard thick roof[J]. International Journal of Coal Science&Technology,2015,2(1):91-96.
[3] DU Wenfeng,PENG Suping,ZHU Guowei,et al. Time-lapse geophysical technology-based study on overburden strata changes induced by modern coal mining[J].International Journal of Coal Science&Technology,2014,1(2):184-191.
[4]李肖音,高峰,钟卫平.基于板模型的采场顶板破断机理分析[J].采矿与安全工程学报,2008,25(2):180-183.LI Xiaoyin,GAO Feng,ZHONG Weiping. Analysis of fracturing mechanism of stope roof based on plate model[J]. Journal of Mining&Safety Engineering,2008,25(2):180-183.
[5]蒋金泉.采场围岩应力与运动[M].北京:煤炭工业出版社,1993.
[6]何富连,赵计生,姚志昌.采场岩层控制论[M].北京:冶金工业出版,2009:6-33.
[7]谢生荣,陈冬冬,孙颜顶,等.基本顶弹性基础边界薄板模型分析(I)——初次破断[J].煤炭学报,2016,41(6):1360-1368.XIE Shengrong,CHEN Dongdong,SUN Yanding,et al. Analysis on thin plate model of basic roof at elastic foundation boundary(I):First breaking[J]. Journal of China Coal Society,2016,41(6):1360-1368.
[8]蒋金泉,张培鹏,秦广鹏,等.一侧采空高位硬厚关键层破断规律与微震能量分布[J].采矿与安全工程学报,2015,32(4):523-529.JIANG Jinquan,ZHANG Peipeng,QIN Guangpeng. Fracture laws of one-side mined high-position hard thick key strata and microseismic energy distribution[J]. Journal of Mining&Safety Engineering,2015,32(4):523-529.
[9]陈冬冬,何富连,谢生荣,等.一侧采空(煤柱)弹性基础边界基本顶薄板初次破断[J].煤炭学报,2017,42(10):2528-2536.CHEN Dongdong,HE Fulian,XIE Shengrong,et al. First fracture of the thin plate of main roof with three sides elastic foundation boundary and one side coal pillar[J].Journal of China Coal Society,2017,42(10):2528-2536.
[10]庞绪峰,蔡来生.孤岛工作面坚硬顶板破断的能量特征研究[J].煤炭工程,2015,47(5):94-97.PANG Xufeng,CAI Laisheng. Study on energy characteristics of hard roof fracture in island working face[J]. Coal Engineering,2015,47(5):94-97.
[11]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,2015,41(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,2015,41(1):36-45.
[12]张益东,张弛,樊志强,等.基于板模型的孤岛工作面主关键层破断机理分析[J].煤炭工程,2010(9):59-62.
[13]刘正春,李伟利.孤岛工作面顶板破断的薄板模型分析[J].矿业安全与环保,2014,41(2):104-106.LIU Zhengchun,LI Weili.Sheet model analysis of roof rupture in island working face[J]. Mining Safety&Environmental Protection,2014,41(2):104-106.
[14]刘宏军.双侧采空孤岛煤体冲击地压发生机理与防治技术研究[D].北京:中国矿业大学(北京),2016.
[15]邓康宇.孙瞳矿1026孤岛采场覆岩运动规律及矿压显现研究[D].淮南:安徽理工大学,2016.
[16]徐芝纶.弹性力学(下册)[M].北京:高等教育出版社,2006:1-13,48-59.
[17]李荣华.偏微分方程数值解法(第2版)第二版[M].北京:高等教育出版社,2010.
[18]姜健飞,吴笑千,胡良剑.数值分析及其MATLAB实验(第2版)[M].北京:清华大学出版社,2015.
[19] QIAO Jianyong.On the preimages of parabolic points[J].Nonlinearity,2000(13):813-818.
[2] KE Yang,HE Xiang,DOU Litong,et al.Experimental investigation into stress-relief characteristics with upward large height and upward mining under hard thick roof[J]. International Journal of Coal Science&Technology,2015,2(1):91-96.
[3] DU Wenfeng,PENG Suping,ZHU Guowei,et al. Time-lapse geophysical technology-based study on overburden strata changes induced by modern coal mining[J].International Journal of Coal Science&Technology,2014,1(2):184-191.
[4]李肖音,高峰,钟卫平.基于板模型的采场顶板破断机理分析[J].采矿与安全工程学报,2008,25(2):180-183.LI Xiaoyin,GAO Feng,ZHONG Weiping. Analysis of fracturing mechanism of stope roof based on plate model[J]. Journal of Mining&Safety Engineering,2008,25(2):180-183.
[5]蒋金泉.采场围岩应力与运动[M].北京:煤炭工业出版社,1993.
[6]何富连,赵计生,姚志昌.采场岩层控制论[M].北京:冶金工业出版,2009:6-33.
[7]谢生荣,陈冬冬,孙颜顶,等.基本顶弹性基础边界薄板模型分析(I)——初次破断[J].煤炭学报,2016,41(6):1360-1368.XIE Shengrong,CHEN Dongdong,SUN Yanding,et al. Analysis on thin plate model of basic roof at elastic foundation boundary(I):First breaking[J]. Journal of China Coal Society,2016,41(6):1360-1368.
[8]蒋金泉,张培鹏,秦广鹏,等.一侧采空高位硬厚关键层破断规律与微震能量分布[J].采矿与安全工程学报,2015,32(4):523-529.JIANG Jinquan,ZHANG Peipeng,QIN Guangpeng. Fracture laws of one-side mined high-position hard thick key strata and microseismic energy distribution[J]. Journal of Mining&Safety Engineering,2015,32(4):523-529.
[9]陈冬冬,何富连,谢生荣,等.一侧采空(煤柱)弹性基础边界基本顶薄板初次破断[J].煤炭学报,2017,42(10):2528-2536.CHEN Dongdong,HE Fulian,XIE Shengrong,et al. First fracture of the thin plate of main roof with three sides elastic foundation boundary and one side coal pillar[J].Journal of China Coal Society,2017,42(10):2528-2536.
[10]庞绪峰,蔡来生.孤岛工作面坚硬顶板破断的能量特征研究[J].煤炭工程,2015,47(5):94-97.PANG Xufeng,CAI Laisheng. Study on energy characteristics of hard roof fracture in island working face[J]. Coal Engineering,2015,47(5):94-97.
[11]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,2015,41(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,2015,41(1):36-45.
[12]张益东,张弛,樊志强,等.基于板模型的孤岛工作面主关键层破断机理分析[J].煤炭工程,2010(9):59-62.
[13]刘正春,李伟利.孤岛工作面顶板破断的薄板模型分析[J].矿业安全与环保,2014,41(2):104-106.LIU Zhengchun,LI Weili.Sheet model analysis of roof rupture in island working face[J]. Mining Safety&Environmental Protection,2014,41(2):104-106.
[14]刘宏军.双侧采空孤岛煤体冲击地压发生机理与防治技术研究[D].北京:中国矿业大学(北京),2016.
[15]邓康宇.孙瞳矿1026孤岛采场覆岩运动规律及矿压显现研究[D].淮南:安徽理工大学,2016.
[16]徐芝纶.弹性力学(下册)[M].北京:高等教育出版社,2006:1-13,48-59.
[17]李荣华.偏微分方程数值解法(第2版)第二版[M].北京:高等教育出版社,2010.
[18]姜健飞,吴笑千,胡良剑.数值分析及其MATLAB实验(第2版)[M].北京:清华大学出版社,2015.
[19] QIAO Jianyong.On the preimages of parabolic points[J].Nonlinearity,2000(13):813-818.