基于能量法的露天开采下采空区顶板安全厚度研究
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摘要
为了确定露天开采下采空区顶板安全厚度,基于力学理论,分析了露天开采下采空区顶板受力特性,建立其固支梁力学结构模型。根据能量守恒原理,推导了由顶板弯曲应变能、水平荷载做功和垂直均布荷载做功组成的采空区顶板结构总能量方程,获得了采空区顶板势能函数解析式。采用突变理论,建立了采空区顶板系统的尖点突变模型,获得了采空区顶板失稳判别式,推导出采空区顶板安全厚度计算模型。对某露天矿采空区顶板厚度进行了应用案例分析,理论计算出的最终采空区顶板临界厚度为11.34 m,与现场安全预警经验值12 m基本一致。表明所建立的采空区顶板安全厚度计算模型合理可行,可为露天开采下采空区顶板安全厚度设计提供一定的理论依据和工程指导。
To determine the safety thickness of goaf roof under open pit mining,based on the mechanics theory,the stress characteristics of goaf roof under open pit mining was analyzed,and the mechanical structure model of clamped-clamped beam was established.The equation describing total energy of goaf roof structure was derived from the energy conservation law,noted that the total energy was taken account of roof bending strain energy,horizontal load work and vertical uniform load work,and the potential energy function of the goaf roof was obtained.Based on the catastrophe theory,the cusp catastrophe model for the system of goaf roof was built,the criterion of instability of goaf roof was obtained,and also the computational model of the safety thickness of goaf roof was conducted.According to an application case study on the safety thickness of goaf roof of an open-pit mine,the final critical thickness of goaf roof was 11.34 m in theoretical calculation,which is basically the same as the site safety warning of empirical value 12 m.The results show that the computational model of the safety thickness of goaf roof is reasonable and feasible,which provides a theoretical basis and engineering guidance for the design of the safety thickness of goaf roof under open pit mining.
To determine the safety thickness of goaf roof under open pit mining,based on the mechanics theory,the stress characteristics of goaf roof under open pit mining was analyzed,and the mechanical structure model of clamped-clamped beam was established.The equation describing total energy of goaf roof structure was derived from the energy conservation law,noted that the total energy was taken account of roof bending strain energy,horizontal load work and vertical uniform load work,and the potential energy function of the goaf roof was obtained.Based on the catastrophe theory,the cusp catastrophe model for the system of goaf roof was built,the criterion of instability of goaf roof was obtained,and also the computational model of the safety thickness of goaf roof was conducted.According to an application case study on the safety thickness of goaf roof of an open-pit mine,the final critical thickness of goaf roof was 11.34 m in theoretical calculation,which is basically the same as the site safety warning of empirical value 12 m.The results show that the computational model of the safety thickness of goaf roof is reasonable and feasible,which provides a theoretical basis and engineering guidance for the design of the safety thickness of goaf roof under open pit mining.
引文
[1]王树仁,贾会会,武崇福.动荷载作用下采空区顶板安全厚度确定方法及其工程应用[J].煤炭学报,2010,35(8):1263-1268.Wang Shuren,Jia Huihui,Wu Chongfu.Determination method of roof safety thickness in the mined-out regions under dynamic loading and its application[J].Journal of China Coal Society,2010,35(8):1263-1268.
[2]燕恩科,姚国栋,万忠明.露天矿采空区顶板最小安全厚度研究[J].化工矿物与加工,2011,40(5):23-25.Ye Enke,Yao Guodong,Wan Zhongming.Study of the minimum safety thickness of the underground goaf[J].Industrial Minerals&Processing,2011,40(5):23-25.
[3]周晓超,侯克鹏.基于改进梁模型的地下空区顶板安全厚度分析[J].矿冶,2014,23(1):21-25.Zhou Xiaochao,Hou Kepeng.Analysis of roof safety thickness of the underground goaf based on improved beam model[J].Mining&Metallurgy,2014,23(1):21-25.
[4]林杭,曹平,李江腾,等.采空区临界安全顶板预测的厚度折减法[J].煤炭学报,2009,34(1):53-57.Lin Hang,Cao Ping,Li Jiangteng,et al.The thickness reduction method in forecasting the critical safety roof thickness of gob area[J].Journal of China Coal Society,2009,34(1):53-57.
[5]张敏思,朱万成,侯召松,等.空区顶板安全厚度和临界跨度确定的数值模拟[J].采矿与安全工程学报,2012,29(4):543-548.Zhang Minsi,Zhu Wancheng,Hou Zhaosong,et al.Numerical simulation for determining the safe roof thickness and critical goaf span[J].Journal of Mining&Safety Engineering,2012,29(4):543-548.
[6]邓鹏宏,王海龙.车辆荷载作用下露天矿采空区顶板安全厚度研究[J].金属矿山,2016(3):62-66.Deng Penghong,Wang Hailong.Study on safety thickness of goafroof under the vehicle load in open-pit iron mine[J].Metal Mine,2016(3):62-66.
[7]何忠明,彭振斌,曹平,等.双层空区开挖顶板稳定性的FLAC3D数值分析[J].中南大学学报:自然科学版,2009,40(4):1066-1071.He Zhongming,Peng Zhenbin,Cao Ping,et al.Numerical analysis for roof stability of double gob area after excavation by FLAC3D[J].Journal of Central South University:Science and Technology,2009,40(4):1066-1071.
[8]柳小波,安龙,张凤鹏.基于薄板理论的空区顶板稳定性分析[J].东北大学学报:自然科学版,2012,33(11):1628-1632.Liu Xiaobo,An Long,Zhang Fengpeng.Analysis on roof stability of gob area based on thin plate theory[J].Journal of Northeastern University:Natural Science,2012,33(11):1628-1632.
[9]甄云军,陈开翔,刘应发,等.地下采空区顶板安全厚度的确定[J].化工矿物与加工,2007,36(9):19-20.Zhen Yunjun,Chen Kaixiang,Liu Yingfa,et al.Determination of roof safety thickness for underground mined-out area[J].Industrial Minerals&Processing,2007,36(9):19-20.
[10]赵康,鄢化彪,冯萧,等.基于能量法的矿柱稳定性分析[J].力学学报,2016,48(4):976-983.Zhao Kang,Yan Huabiao,Feng Xiao,et al.Stability analysis of pillar based on energy law[J].Chinese Journal of Theoretical and Applied Mechanics,2016,48(4):976-983.
[11]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 Siqing Wang Sijing.Instability leading to rockbursts and nonlinear evolutionary mechanisms for coal-pillar-and-roof system[J].Journal of Engineering Geology,2005,13(4):437-446.
[12]闫长斌,徐国元.动荷载诱发上下交叠硐室间顶柱失稳的突变理论分析[J].工程力学,2007,24(4):46-51.Yan Changbin,Xu Guoyuan.Analysis on instability of the top pillar between overlap underground chambers induced by danymic loadings with catastrophy theory[J].Engineering Mechanics,2007,24(4):46-51.
[13]任智敏.基于尖点突变理论的大跨度巷道顶板稳定性分析[J].中国矿业,2014,23(10):111-114.Ren Zhimin.Stability analysis of large-span roadway roof based on cusp catastrophe theory[J].China Mining Magazine,2014,23(10):111-114.
[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.
[15]赵延林,吴启红,王卫军,等.基于突变理论的采空区重叠顶板稳定性强度折减法及应用[J].岩石力学与工程学报,2010,29(7):1424-1434.Zhao Yanlin,Wu Qihong,Wang Weijun,et al.Strength reduction method to study stability of goaf overlapping roof based on catastrophe theory[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(7):1424-1434.
[16]马莎,肖明.基于突变理论和监测位移的地下洞室稳定评判方法[J].岩石力学与工程学报,2010,29(S2):3812-3819.Ma Sha,Xiao Ming.Judgment method for stability of underground cavern based on catastrophe theory and monitoring displacement[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(S2):3812-3819.
[17]郑东健,雷霆.基于突变理论的高拱坝失稳判据研究[J].岩土工程学报,2011,33(1):23-27.Zheng Dongjian,Lei Ting.Instability criteria for high arch dams using catastrophe theory[J].Chinese Journal of Geotechnical Engineering,2011,33(1):23-27.
[18]杨治林.回采巷道底板岩层结构的后屈曲性态研究[J].煤炭学报,2011,36(S2):278-281.Yang Zhilin.Post-buckling behavior of floor strata structure for extraction roadway[J].Journal of China Coal Society,2011,36(S2):278-281.
[19]邵爱军,彭建萍,刘唐生.矿坑底板突水的突变模型研究[J].岩土工程学报,2001,23(1):38-41.Shao Aijun,Peng Jianping,Liu Tangsheng.Research on a cusp catastrophic model of water bursting in pit floors[J].Chinese Journal of Geotechnical Engineering,2001,23(1):38-41.
[20]张建文,王树仁,贾会会,等.地面施工载荷对采空区顶板变形破坏效应分析[J].煤炭科学技术,2010,38(9):19-22.Zhang Jianwen,Wang Shuren,Jia Huihui,et al.Analysis on construction loading at surface ground to roof deformation failure effect in goaf of underground mining[J].Coal Science and Technology,2010,38(9):19-22.
[21]Zhao Wangchun,Wang Tingting,Ju Guoshuai,et al.The study on fractal damage of rock under hydraulic fracturing basing on conversation of energy[J].Applied Mechanics&Materials,2010,29/32:1363-1368.
[22]罗斌玉,叶义成,胡南燕,等.基于应变能平衡的条带矿柱破裂宽度及其影响因素[J].金属矿山,2016(8):48-53.Luo Binyu,Ye Yicheng,Hu Nanyan,et al.Width of fractured zone of strip pillars based on the strain energy balance theory and Its influencing factors[J].Metal Mine,2016(8):48-53.
[23]Wang Zhiqiang,Li Aiwu,Pan Yue.Energy Releasing Illustration of Rock Destabilization Based on Catastrophe Theory[J].Advanced Materials Research,2011,261/263:947-951.
[24]潘岳,王志强,张勇.突变理论在岩体系统动力失稳中的应用[M].北京:科学出版社,2008:4-6.Pan Yue,Wang Zhiqiang,Zhang Yong.Application of Catastrophe Theory to the Dynamic Stability Loss of Rock Mass System[M].Beijing:Science Press,2008:4-6.
[2]燕恩科,姚国栋,万忠明.露天矿采空区顶板最小安全厚度研究[J].化工矿物与加工,2011,40(5):23-25.Ye Enke,Yao Guodong,Wan Zhongming.Study of the minimum safety thickness of the underground goaf[J].Industrial Minerals&Processing,2011,40(5):23-25.
[3]周晓超,侯克鹏.基于改进梁模型的地下空区顶板安全厚度分析[J].矿冶,2014,23(1):21-25.Zhou Xiaochao,Hou Kepeng.Analysis of roof safety thickness of the underground goaf based on improved beam model[J].Mining&Metallurgy,2014,23(1):21-25.
[4]林杭,曹平,李江腾,等.采空区临界安全顶板预测的厚度折减法[J].煤炭学报,2009,34(1):53-57.Lin Hang,Cao Ping,Li Jiangteng,et al.The thickness reduction method in forecasting the critical safety roof thickness of gob area[J].Journal of China Coal Society,2009,34(1):53-57.
[5]张敏思,朱万成,侯召松,等.空区顶板安全厚度和临界跨度确定的数值模拟[J].采矿与安全工程学报,2012,29(4):543-548.Zhang Minsi,Zhu Wancheng,Hou Zhaosong,et al.Numerical simulation for determining the safe roof thickness and critical goaf span[J].Journal of Mining&Safety Engineering,2012,29(4):543-548.
[6]邓鹏宏,王海龙.车辆荷载作用下露天矿采空区顶板安全厚度研究[J].金属矿山,2016(3):62-66.Deng Penghong,Wang Hailong.Study on safety thickness of goafroof under the vehicle load in open-pit iron mine[J].Metal Mine,2016(3):62-66.
[7]何忠明,彭振斌,曹平,等.双层空区开挖顶板稳定性的FLAC3D数值分析[J].中南大学学报:自然科学版,2009,40(4):1066-1071.He Zhongming,Peng Zhenbin,Cao Ping,et al.Numerical analysis for roof stability of double gob area after excavation by FLAC3D[J].Journal of Central South University:Science and Technology,2009,40(4):1066-1071.
[8]柳小波,安龙,张凤鹏.基于薄板理论的空区顶板稳定性分析[J].东北大学学报:自然科学版,2012,33(11):1628-1632.Liu Xiaobo,An Long,Zhang Fengpeng.Analysis on roof stability of gob area based on thin plate theory[J].Journal of Northeastern University:Natural Science,2012,33(11):1628-1632.
[9]甄云军,陈开翔,刘应发,等.地下采空区顶板安全厚度的确定[J].化工矿物与加工,2007,36(9):19-20.Zhen Yunjun,Chen Kaixiang,Liu Yingfa,et al.Determination of roof safety thickness for underground mined-out area[J].Industrial Minerals&Processing,2007,36(9):19-20.
[10]赵康,鄢化彪,冯萧,等.基于能量法的矿柱稳定性分析[J].力学学报,2016,48(4):976-983.Zhao Kang,Yan Huabiao,Feng Xiao,et al.Stability analysis of pillar based on energy law[J].Chinese Journal of Theoretical and Applied Mechanics,2016,48(4):976-983.
[11]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 Siqing Wang Sijing.Instability leading to rockbursts and nonlinear evolutionary mechanisms for coal-pillar-and-roof system[J].Journal of Engineering Geology,2005,13(4):437-446.
[12]闫长斌,徐国元.动荷载诱发上下交叠硐室间顶柱失稳的突变理论分析[J].工程力学,2007,24(4):46-51.Yan Changbin,Xu Guoyuan.Analysis on instability of the top pillar between overlap underground chambers induced by danymic loadings with catastrophy theory[J].Engineering Mechanics,2007,24(4):46-51.
[13]任智敏.基于尖点突变理论的大跨度巷道顶板稳定性分析[J].中国矿业,2014,23(10):111-114.Ren Zhimin.Stability analysis of large-span roadway roof based on cusp catastrophe theory[J].China Mining Magazine,2014,23(10):111-114.
[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.
[15]赵延林,吴启红,王卫军,等.基于突变理论的采空区重叠顶板稳定性强度折减法及应用[J].岩石力学与工程学报,2010,29(7):1424-1434.Zhao Yanlin,Wu Qihong,Wang Weijun,et al.Strength reduction method to study stability of goaf overlapping roof based on catastrophe theory[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(7):1424-1434.
[16]马莎,肖明.基于突变理论和监测位移的地下洞室稳定评判方法[J].岩石力学与工程学报,2010,29(S2):3812-3819.Ma Sha,Xiao Ming.Judgment method for stability of underground cavern based on catastrophe theory and monitoring displacement[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(S2):3812-3819.
[17]郑东健,雷霆.基于突变理论的高拱坝失稳判据研究[J].岩土工程学报,2011,33(1):23-27.Zheng Dongjian,Lei Ting.Instability criteria for high arch dams using catastrophe theory[J].Chinese Journal of Geotechnical Engineering,2011,33(1):23-27.
[18]杨治林.回采巷道底板岩层结构的后屈曲性态研究[J].煤炭学报,2011,36(S2):278-281.Yang Zhilin.Post-buckling behavior of floor strata structure for extraction roadway[J].Journal of China Coal Society,2011,36(S2):278-281.
[19]邵爱军,彭建萍,刘唐生.矿坑底板突水的突变模型研究[J].岩土工程学报,2001,23(1):38-41.Shao Aijun,Peng Jianping,Liu Tangsheng.Research on a cusp catastrophic model of water bursting in pit floors[J].Chinese Journal of Geotechnical Engineering,2001,23(1):38-41.
[20]张建文,王树仁,贾会会,等.地面施工载荷对采空区顶板变形破坏效应分析[J].煤炭科学技术,2010,38(9):19-22.Zhang Jianwen,Wang Shuren,Jia Huihui,et al.Analysis on construction loading at surface ground to roof deformation failure effect in goaf of underground mining[J].Coal Science and Technology,2010,38(9):19-22.
[21]Zhao Wangchun,Wang Tingting,Ju Guoshuai,et al.The study on fractal damage of rock under hydraulic fracturing basing on conversation of energy[J].Applied Mechanics&Materials,2010,29/32:1363-1368.
[22]罗斌玉,叶义成,胡南燕,等.基于应变能平衡的条带矿柱破裂宽度及其影响因素[J].金属矿山,2016(8):48-53.Luo Binyu,Ye Yicheng,Hu Nanyan,et al.Width of fractured zone of strip pillars based on the strain energy balance theory and Its influencing factors[J].Metal Mine,2016(8):48-53.
[23]Wang Zhiqiang,Li Aiwu,Pan Yue.Energy Releasing Illustration of Rock Destabilization Based on Catastrophe Theory[J].Advanced Materials Research,2011,261/263:947-951.
[24]潘岳,王志强,张勇.突变理论在岩体系统动力失稳中的应用[M].北京:科学出版社,2008:4-6.Pan Yue,Wang Zhiqiang,Zhang Yong.Application of Catastrophe Theory to the Dynamic Stability Loss of Rock Mass System[M].Beijing:Science Press,2008:4-6.