基于Mohr-Coulomb准则的缓倾斜层状矿床矿柱强度估算及倾角效应
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摘要
矿柱强度是评估矿柱稳定性的重要因素之一,矿柱的稳定是地下矿床安全开采的基础。以弹性力学理论为基础,分析了缓倾斜层状矿床中矿柱的受力状态,应用图解法绘制出表征矿柱应力状态的广义莫尔圆。根据应力圆与Mohr-Coulomb强度包络线之间的关系,建立了矿柱强度解析式,分析了莫尔圆圆心所在直线斜率tan_β随矿体倾角的变化特性,并结合数值模拟,研究矿体倾角效应对矿柱强度的影响。研究表明:应力圆圆心所在直线斜率tan_β是矿体倾角θ及侧压系数λ的二元函数,当tan_β取得最大值时,矿柱强度最小;当矿柱宽高比w_p/h_p保持一定且矿体倾角在5°～45°区间时,随着矿体倾角增大,矿柱强度逐渐减小。研究可为缓倾斜层状矿床矿柱强度估算提供参考。
Pillar strength is one of the important factors for evaluating the pillar stability, which is the basis for safe mining for underground deposits. In this paper, the stress state of pillars in gently inclined layered deposits was analyzed under the combined action of normal stress and shear stress using the theory of elastic mechanics, and a generalized Mohr's circle was plotted by graphic method to characterize the stress state of the pillars. According to the relationship between the generalized stress circle and the Mohr-Coulomb strength envelope, an analytic formula for the pillar strength was developed to analyze the variation of the slope of straight line( tan_β) at the center of Mohr circle with the dip angle of ore body. The influence of the ore-body inclination on the pillar strength was also analyzed by numerical simulation. Result shows that tan_β is a binary function of the deposit angle θ and the lateral pressure coefficient λ. When the maximum value of tan_β is obtained, the strength of the pillar is the smallest. When the w_p/h_p of the pillar keeps a same value and the ore body dip angle is within 5°～45°, the strength of the pillar gradually decreases with the increase of the dip of the ore body. The study can provide a reference for the estimation of the strength of the pillars in gently inclined bedded deposits.
Pillar strength is one of the important factors for evaluating the pillar stability, which is the basis for safe mining for underground deposits. In this paper, the stress state of pillars in gently inclined layered deposits was analyzed under the combined action of normal stress and shear stress using the theory of elastic mechanics, and a generalized Mohr's circle was plotted by graphic method to characterize the stress state of the pillars. According to the relationship between the generalized stress circle and the Mohr-Coulomb strength envelope, an analytic formula for the pillar strength was developed to analyze the variation of the slope of straight line( tan_β) at the center of Mohr circle with the dip angle of ore body. The influence of the ore-body inclination on the pillar strength was also analyzed by numerical simulation. Result shows that tan_β is a binary function of the deposit angle θ and the lateral pressure coefficient λ. When the maximum value of tan_β is obtained, the strength of the pillar is the smallest. When the w_p/h_p of the pillar keeps a same value and the ore body dip angle is within 5°～45°, the strength of the pillar gradually decreases with the increase of the dip of the ore body. The study can provide a reference for the estimation of the strength of the pillars in gently inclined bedded deposits.
引文
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[12]朱建明,彭新坡,姚仰平,等.SMP准则在计算煤柱极限强度中的应用[J].岩土力学,2010,31(9):2987-2990.ZHU Jian-ming,PENG Xin-po,YAO Yang-ping,et al.Application of SMP failure criterion to computing limit strength of coal pillars[J].Rock and Soil Mechanics,2010,31(9):2987-2990.
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[17]李学华,姚强岭,张有乾.考虑层间剪应力作用的煤矿岩层控制理论探讨[J].岩土力学,2018,39(7):2371-2378.LI Xue-hua,YAO Qiang-ling,ZHANG You-qian.Study of theory of minestrata control based on shear stress between stratum[J].Rock and Soil Mechanics,2018,39(7):2371-2378.
[18]刘晓云,叶义成,王其虎,等.单轴压缩下不同强度组合复合岩体相似材料试件力学特性研究[J].岩土力学,2017,38(增刊2):183-190.LIU Xiao-yun,YE Yi-cheng,WANG Qi-hu,et al.Mechanical properties of similar material specimens of composite rock masses with different strengths under uniaxial compression[J].Rock and Soil Mechanics,2017,38(Suppl.2):183-190.
[19]PARISEAU W G.Design analysis in rock mechanics,second edition[M].[S.l.]:CRC Press,2011.
[20]MATHEY M,MERWE J N V D.Critique of the South African squat coal pillar strength formula[J].Journal of the Southern African Institute of Mining&Metallurgy,2016,116(3):291-299.
[21]GALVIN B J M.Ground engineering-principles and practices for underground coal mining[M].Zurich:Springer International Publishing,2016.
[22]DAS M N.Influence of width/height ratio on post-failure behaviour of coal[J].International Journal of Mining&Geological Engineering,1986,4(1):79-87.
[2]钱鸣高,许家林,缪协兴,等.煤矿绿色开采技术[J].中国矿业大学学报,2003,32(4):343-348.QIAN Ming-gao,XU Jia-lin,MIAO Xie-xing,et al.Green technique in coal mining[J].Journal of China University of Mining&Technology,2003,32(4):343-348.
[3]王旭春,黄福昌,张怀新,等.A.H.威尔逊煤柱设计公式探讨及改进[J].煤炭学报,2002,27(6):604-608.WUANG Xu-chun,HUANG Fu-chang,ZHANGHuai-xin,et al.Discussion and improvement for A.H.Wilson coal pillar design[J].Journal of China Coal Society,2002,27(6):604-608.
[4]刘贵,张华兴,徐乃忠.深部厚煤层条带开采煤柱的稳定性[J].煤炭学报,2008,33(10):1086-1091.LIU Gui,ZHANG Hua-xing,XU Nai-zhong.Coal pillar stability of deep and high seam strip-partial mining[J].Journal of China Coal Society,2008,33(10):1086-1091.
[5]SHEOREY P R,DAS M N,BORDIA S K,et al.Pillar strength approaches based on a new failure criterion for coal seams[J].International Journal of Mining&Geological Engineering,1986,4(4):273-290.
[6]SHEOREY P R,BISWAS A K,CHOUBEY V D.An empirical failure criterion for rocks and jointed rock masses[J].Engineering Geology,1989,26(2):141-159.
[7]JAISWAL A,SHRIVASTVA B K.Numerical simulation of coal pillar strength[J].International Journal of Rock Mechanics&Mining Sciences,2009,46(4):779-788.
[8]SALAMON M D G,CANBULAT I,RYDER J A.Seam-specific pillar strength formulae for South African collieries[C]//Proceedings of the 41st U.S.Rock Mechanics Symposium.Alexandria:[s.n.],2006:1142-1154.
[9]LUNDER P J,PAKALNIS R C.Determination of the strength of hard-rock mine pillars[J].World Mining Express,1998,14(4):51-55.
[10]BERTUZZI R,DOUGLAS K,MOSTYN G.An approach to model the strength of coal pillars[J].International Journal of Rock Mechanics&Mining Sciences,2016,89:165-175.
[11]MORTAZAVI A,HASSANI F P,SHABANI M.Anumerical investigation of rock pillar failure mechanism in underground openings[J].Computers&Geotechnics,2009,36(5):691-697.
[12]朱建明,彭新坡,姚仰平,等.SMP准则在计算煤柱极限强度中的应用[J].岩土力学,2010,31(9):2987-2990.ZHU Jian-ming,PENG Xin-po,YAO Yang-ping,et al.Application of SMP failure criterion to computing limit strength of coal pillars[J].Rock and Soil Mechanics,2010,31(9):2987-2990.
[13]ESTERHUIZEN G S,DOLINAR D R,ELLENBERGERJ L.Pillar strength in underground stone mines in the United States[J].International Journal of Rock Mechanics&Mining Sciences,2011,48(1):42-50.
[14]郭力群,彭兴黔,蔡奇鹏.基于统一强度理论的条带煤柱设计[J].煤炭学报,2013,38(9):1563-1567.GUO Li-qun,PENG Xing-qian,CAI Qi-peng.Design of strip coal pillar based on the unified strength theory[J].Journal of China Coal Society,2013,38(9):1563-1567.
[15]郭力群,蔡奇鹏,彭兴黔.条带煤柱设计的强度准则效应研究[J].岩土力学,2014,35(3):777-782.GUO Li-qun,CAI Qi-peng,PENG Xing-qian.Effect of strength criterion on design of strip coal pillar[J].Rock and Soil Mechanics,2014,35(3):777-782.
[16]LORIG L J.Pillar strength estimates for foliated and inclined pillars in schistose material[C]//Proceedings of the 3rd International FLAC/DEM Symposium.Hangzhou:[s.n.],2013:1-7.
[17]李学华,姚强岭,张有乾.考虑层间剪应力作用的煤矿岩层控制理论探讨[J].岩土力学,2018,39(7):2371-2378.LI Xue-hua,YAO Qiang-ling,ZHANG You-qian.Study of theory of minestrata control based on shear stress between stratum[J].Rock and Soil Mechanics,2018,39(7):2371-2378.
[18]刘晓云,叶义成,王其虎,等.单轴压缩下不同强度组合复合岩体相似材料试件力学特性研究[J].岩土力学,2017,38(增刊2):183-190.LIU Xiao-yun,YE Yi-cheng,WANG Qi-hu,et al.Mechanical properties of similar material specimens of composite rock masses with different strengths under uniaxial compression[J].Rock and Soil Mechanics,2017,38(Suppl.2):183-190.
[19]PARISEAU W G.Design analysis in rock mechanics,second edition[M].[S.l.]:CRC Press,2011.
[20]MATHEY M,MERWE J N V D.Critique of the South African squat coal pillar strength formula[J].Journal of the Southern African Institute of Mining&Metallurgy,2016,116(3):291-299.
[21]GALVIN B J M.Ground engineering-principles and practices for underground coal mining[M].Zurich:Springer International Publishing,2016.
[22]DAS M N.Influence of width/height ratio on post-failure behaviour of coal[J].International Journal of Mining&Geological Engineering,1986,4(1):79-87.