阶段空场嗣后充填体三维拱应力及强度需求模型
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摘要
在地下厚大金属矿体的两步骤阶段空场嗣后充填采矿法中,合理平衡一步骤矿房采场胶结充填体的揭露稳定性及其强度需求对安全经济充填采矿影响重大。为获取该采矿法中胶结充填体强度需求的三维解析模型与方法,解决类似矿山确定充填体强度需求主要采用经验类比、缺乏科学合理计算方法的问题,本文借鉴土力学应力拱理论,分析了两步骤采充时序过程中的相邻采场充填体空间接触关系,分别研究了二步骤采场非胶结充填体、一步骤采场胶结充填体(揭露后)的应力分布模式,基于Marston拱应力二维模型,拓展建立了各采场充填体的三维拱应力解析模型,得出了非胶结充填体-胶结充填体-采场围岩之间的应力传递规律及接触力学边界解析方法,并通过FLAC3D模拟的拱应力分布结果进行了三维拱应力解析模型的对比验证。进一步将提出的拱应力解析方法应用至Mitchell强度需求解析模型中,考虑了三维成拱作用下非胶结充填体对胶结充填体的侧向推力作用、采场上下盘围岩对胶结充填体的接触摩擦作用,以底部滑动面方向角、滑动体与围岩接触面摩擦力方向角的不同取值情况,定量表征了揭露后胶结充填体的潜在破坏模式,并据此提出了4种胶结充填体安全系数和强度需求的三维解析模型与方法。再利用FLAC3D开展了不同采场尺寸(长度、宽度、高度)、不同充填体参数(容重、内摩擦角)等条件下的充填体强度需求数值解搜索计算,与4种解析方法计算的强度需求结果进行了对比验证,得出了当胶结充填体底部滑动面方向角α=45°+φ_c/2且滑动体与围岩接触面摩擦力方向角β=45°-φ_c/2时,胶结充填体强度需求的三维解析解和三维数值解吻合度最佳,最终获取了最优的一步骤采场胶结充填体强度需求三维解析模型与方法。
In two steps open stoping with subsequent backfill mining method for underground thick metal ore bodies,a reasonable balance between the stability and strength requirement of the exposed cemented backfill in primary stopes has significant effects on the safe and economic mining operations. In order to build a reasonable three-dimensional analytical model and method for estimating the strength requirement of cemented backfill in this mining method,and solve the problems that empirical analogy is usually applied to determine the required strength of backfill for the lack of scientific and reasonable calculation methods,the spatial contact properties of the backfills in adjacent stopes in the processes of excavating and filling have been analyzed based on the arching theory borrowed from soil mechanics.Stress distributions of the uncemented backfill in secondary stopes and the exposed cemented backfill in primary stopes have been investigated separately. Three-dimensional analytical models for the arching stress of these backfills have been developed from Marston two-dimensional arching stress model,to reveal the stress transfer laws and quantitative characterization methods of these contact boundaries among the uncemented backfill in secondary stopes,cemented backfill in primary stopes and surrounding rock. The analytical results of arching stress have been compared and verified against the numerical arching stress through FLAC3D simulations. The proposed analytical models of arching stress are further applied to Mitchell model of strength requirements evaluation. The three-dimensional arching lateral pressure from the uncemented backfill acting on the exposed cemented backfill,and the contact friction between the cemented backfill and surrounding rock masses have been considered. The potential failure modes of exposed cemented backfill are quantitatively characterized by the different values of direction angles of sliding plane and the frictional force along the interfaces between the cemented backfill and surrounding rock masses. Four kinds of three-dimensional analytical models and methods for the safety factor and strength requirement of cemented backfill are proposed based on these failure modes. Numerical solution search and calculation of backfill strength requirements have been carried with FLAC3D under different stope sizes(length,width,height) and different backfill parameters(bulk density,internal friction angle),to compare and verify the proposed four kinds of three-dimensional analytical solutions. The analytical and numerical solutions for the strength requirements of cemented backfill have the best consistency when the direction angle of the sliding planeα=45°+φ_c tween the cemented backfill and surrounding rock masses β= 45°-φ_c model and method for the strength requirements of the cemented backfill in primary stopes have been obtained.
In two steps open stoping with subsequent backfill mining method for underground thick metal ore bodies,a reasonable balance between the stability and strength requirement of the exposed cemented backfill in primary stopes has significant effects on the safe and economic mining operations. In order to build a reasonable three-dimensional analytical model and method for estimating the strength requirement of cemented backfill in this mining method,and solve the problems that empirical analogy is usually applied to determine the required strength of backfill for the lack of scientific and reasonable calculation methods,the spatial contact properties of the backfills in adjacent stopes in the processes of excavating and filling have been analyzed based on the arching theory borrowed from soil mechanics.Stress distributions of the uncemented backfill in secondary stopes and the exposed cemented backfill in primary stopes have been investigated separately. Three-dimensional analytical models for the arching stress of these backfills have been developed from Marston two-dimensional arching stress model,to reveal the stress transfer laws and quantitative characterization methods of these contact boundaries among the uncemented backfill in secondary stopes,cemented backfill in primary stopes and surrounding rock. The analytical results of arching stress have been compared and verified against the numerical arching stress through FLAC3D simulations. The proposed analytical models of arching stress are further applied to Mitchell model of strength requirements evaluation. The three-dimensional arching lateral pressure from the uncemented backfill acting on the exposed cemented backfill,and the contact friction between the cemented backfill and surrounding rock masses have been considered. The potential failure modes of exposed cemented backfill are quantitatively characterized by the different values of direction angles of sliding plane and the frictional force along the interfaces between the cemented backfill and surrounding rock masses. Four kinds of three-dimensional analytical models and methods for the safety factor and strength requirement of cemented backfill are proposed based on these failure modes. Numerical solution search and calculation of backfill strength requirements have been carried with FLAC3D under different stope sizes(length,width,height) and different backfill parameters(bulk density,internal friction angle),to compare and verify the proposed four kinds of three-dimensional analytical solutions. The analytical and numerical solutions for the strength requirements of cemented backfill have the best consistency when the direction angle of the sliding planeα=45°+φ_c tween the cemented backfill and surrounding rock masses β= 45°-φ_c model and method for the strength requirements of the cemented backfill in primary stopes have been obtained.
引文
[1]DARLING P.SME mining engineering handbook(Third edition)[M].Denver:Society for Mining,Metallurgy,and Exploration,Colorado,USA,2011.
[2]HASSANI F,ARCHIBALD J.Mine backfill[M].Montreal:Canadian Institute of Mine,Metallurgy and Petroleum,1998.
[3]BELEM T,MBONIMPA M.Minimum strength required for resisting to cyclic softening/failure of cemented paste backfill at early age[A].Proceedings of the 3rd International Symposium on Mine Safety Science and Engineering[C].Montreal,2016.
[4]吴爱祥,沈慧明,姜立春,等.窄长型充填体的拱架效应及其对目标强度的影响[J].中国有色金属学报,2016,26(3):648-653.WU Aixiang,SHEN Huiming,JIANG Lichun,et al.Arching effect of long-narrow cemented paste backfill body and its effect on target strength[J].Chinese Journal of Nonferrous Metals,2016,26(3):648-653.
[5]MITCHELL R J,OLSEN R S,SMITH J D.Model studies on cemented tailings used in mine backfill[J].Canadian Geotechnical Journal,1982,19(1):14-28.
[6]DUNCAN J M,WRIGHT S G.Soil strength and slope stability[M].Hoboken:John Wiley&Sons,2005.
[7]DIRIGE A P E,MCNEARNY R L,THOMPSON D S.The effect of stope inclination and wall rock roughness on back-fill free face stability[A].Rock Engineering in Difficult Conditions,Proceedings of the 3rd Canada-US Rock Mechanics Symposium,DIEDERICHS Mand GRASSELLI G(Eds.)[C].Toronto,2009,4152.
[8]ZOU S,NADARAJAH N.Optimizing backfill design for ground support and cost saving[A].Golden Rocks 2006,the 41st US Symposium on Rock Mechanics(USRMS),American Rock Mechanics Association[C].Golden:2006:7-21.
[9]LI L.Generalized solution for mining backfill design[J].International Journal of Geomechanics,2014,14(3):04014006.
[10]LI L.Analytical solution for determining the required strength of a side-exposed mine backfill containing a plug[J].Canadian Geotechnical Journal,2014,51(5):508-519.
[11]LI L,AUBETIN M.An improved method to assess the required strength of cemented backfill in underground stopes with an open face[J].International Journal of Mining Science and Technology,2014,24(4):549-558.
[12]LIU G S,LI L,YANG X C,et al.Required strength estimation of a cemented backfill with the front wall exposed and back wall pressured[J].International Journal of Mining and Mineral Engineering,2018,9(1):1-20.
[13]曾照凯,张义平,王永明.高阶段采场充填体强度及稳定性研究[J].金属矿山,2010,(1):31-34.ZENG Zhaokai,ZHANG Yiping,WANG Yongming.Research on the strength and stability on fill body of high-bench stope[J].Metal Mine,2010,(1):31-34.
[14]朱志彬,刘成平.充填体强度计算及稳定性分析[J].采矿技术,2008,8(3):15-17,25.ZHU Zhibin,LIU Chengping.Strength calculation and stability analysis of backfill[J].Mining Technology,2008,8(3):15-17,25.
[15]刘志祥,李夕兵,戴塔根,等.尾砂胶结充填体损伤模型及与岩体的匹配分析[J].岩土力学,2006,27(9):1442-1446.LIU Zhixiang,LI Xibing,DAI Tagen,et al.On damage model of cemented tailings backfill and its match with rock mass[J].Rock and Soil Mechanics,2006,27(9):1442-1446.
[16]刘志祥,李夕兵,赵国彦,等.充填体与岩体三维能量耗损规律及合理匹配[J].岩石力学与工程学报,2010,29(2):344-348.LIU Zhixiang,LI Xibing,ZHAO Guoyan,et al.Three dimensional energy dissipation laws and reasonable matches between backfill and rock mass[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(2):344-348.
[17]LIU Z X,LAN M,XIAO S Y,et al.Damage failure of cemented backfill and its reasonable match with rock mass[J].Transactions of Nonferrous Metals Society of China,2015,25(3):954-959.
[18]刘志祥,李夕兵,张义平.基于混沌优化的高阶段充填体可靠性分析[J].岩土工程学报,2006,28(3):348-352.LIU Zhixiang,LI Xibing,ZHANG Yiping.Reliability analysis of high level backfill based on chaotic optimization[J].Chinese Journal of Geotechnical Engineering,2006,28(3):348-352.
[19]刘志祥,刘青灵,周士霖.基于可靠度理论的充填体强度设计[J].矿冶工程,2012,32(6):1-4,8.LIU Zhixiang,LIU Qingling,ZHOU Shilin.Backfill strength design based on reliability theory[J].Mining and Metallurgical Engineering,2012,32(6):1-4,8.
[20]MARSTON A.The theory of external loads on closed conduits in the light of latest experiments[A].Proceedings of the Ninth Annual Meeting of the Highway Research Board[C].Washington,D.C.:1930,9:138-170.
[21]THOMPSON B,BAWDEN W,GRABINSKY M.In situ measurements of cemented paste backfill at the Cayeli Mine[J].Canadian Geotechnical Journal,2012,49(7):755-772.
[22]EIMKADMI N,AUBERTIN M,LI L.Effect of drainage and sequential filling on the behavior of backfill in mine stopes[J].Canadian Geotechnical Journal,2014,51(1):1-15.
[23]LIU G S,LI L,YANG X C,et al.Numerical analysis of stress distribution in backfilled stopes considering interfaces between the backfill and rock walls[J].International Journal of Geomechanics,2017,17(2):06016014.
[24]LIU G S,LI L,YANG X C,et al.A numerical analysis of the stress distribution in backfilled stopes considering nonplanar interfaces between the backfill and rock walls[J].International Journal of Geotechnical Engineering,2016,10(3):271-282.
[25]LIU G S,LI L,YANG X C,et al.Stability analyses of vertically exposed cemented backfill:A revisit to Mitchell’s physical model tests[J].International Journal of Mining Science and Technology,2016,26(6):1135-1144.
[26]刘钦,李地元,刘志祥,等.水平推力作用下抗滑桩间土拱效应影响因素的数值分析[J].中南大学学报(自然科学版),2011,42(7):2071-2077.LIU Qin,LI Diyuan,LIU Zhixiang,et al.Numerical analysis of influence factors on soil arching effect between anti-sliding piles under horizontal pushing loads[J].Journal of Central South University(Science Edition),2011,42(7):2071-2077.
[27]涂兵雄,贾金青.考虑土拱效应的黏性填土挡土墙主动土压力研究[J].岩石力学与工程学报,2012,31(5):1064-1070.TU Bingxiong,JIA Jinqing.Research on active earth pressure behind rigid retaining wall from clayey backfill considering soil arching effects[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(5):1064-1070.
[28]LI L,AUBERTIN J D,DUBE J S.Stress distribution in a cohesionless backfill poured in a silo[J].Open Civil Engineering Journal,2014,8(1):1-8.
[29]GRABINSKY M W,BAWDEN W F.In situ measurements for geomechanical design of cemented paste backfill systems[A].Proceeding of 9th International Symposium in Mining with Backfill[C].Montreal,2007.
[30]LI L,AUBERTIN M,BELEM T.Formulation of a three dimensional analytical solution to evaluate stresses in backfilled vertical narrow openings[J].Canadian Geotechnical Journal,2005,42(6):1705-1717.
[31]PIRAPAKARAN K,SIVAKUGAN N.Arching within hydraulic fill stopes[J].Geotechnical and Geological Engineering,2007,25(1):25-35.
[32]SOBHI M A,LI L,AUBERTIN M.Numerical investigation of earth pressure coefficient along central line of backfilled stopes[J].Canadian Geotechnical Journal,2017,54(1):138-145.
[33]VEESTRA R.A design procedure for determining the in situ stresses of early age cemented paste backfill[D].Toronto:University of Toronto,Canada,2013.
[34]FALAKNAZ N.Analysis of geomechanical behavior of two adjacent backfilled stopes based on two and three dimensional numerical simulations[D].Montréal:Polytechnique Montreal,Canada,2014.
[35]EMAD M Z.Dynamic performance of cemented rockfill under blastinduced vibrations[D].Montréal:McGill University,2013.
[36]刘光生.充填体与围岩接触成拱作用机理及强度模型研究[D].北京:北京科技大学,2017.LIU Guangsheng.Required strength model of cemented backfill with research on arching mechanism considering backfill-rock interaction[D].Beijing:University of Science and Technology Beijing,2017.
[37]LI L,AUBERTIN M.Numerical investigation of the stress state in inclined backfilled Stopes[J].International Journal of Geomechanics,2009,9(2):52-62.
[38]ASKEW J E,MCCARTHY P L,FITZGERALD D J.Backfill research for pillar extraction at ZC/NBHC[A].Mining with Backfill[C].Sudbury:1978:100-110.
[39]ARIOGLU E.Design aspects of cemented aggregate fill mixes for tungsten stoping operations[J].Mining Science and Technology,1984,1(3):209-214.
[40]LIU G S,LI L,YAO M,et al.An investigation of the uniaxial compressive strength of a cemented hydraulic backfill made of alluvial sand[J].Minerals,2017,7(1):4.
[2]HASSANI F,ARCHIBALD J.Mine backfill[M].Montreal:Canadian Institute of Mine,Metallurgy and Petroleum,1998.
[3]BELEM T,MBONIMPA M.Minimum strength required for resisting to cyclic softening/failure of cemented paste backfill at early age[A].Proceedings of the 3rd International Symposium on Mine Safety Science and Engineering[C].Montreal,2016.
[4]吴爱祥,沈慧明,姜立春,等.窄长型充填体的拱架效应及其对目标强度的影响[J].中国有色金属学报,2016,26(3):648-653.WU Aixiang,SHEN Huiming,JIANG Lichun,et al.Arching effect of long-narrow cemented paste backfill body and its effect on target strength[J].Chinese Journal of Nonferrous Metals,2016,26(3):648-653.
[5]MITCHELL R J,OLSEN R S,SMITH J D.Model studies on cemented tailings used in mine backfill[J].Canadian Geotechnical Journal,1982,19(1):14-28.
[6]DUNCAN J M,WRIGHT S G.Soil strength and slope stability[M].Hoboken:John Wiley&Sons,2005.
[7]DIRIGE A P E,MCNEARNY R L,THOMPSON D S.The effect of stope inclination and wall rock roughness on back-fill free face stability[A].Rock Engineering in Difficult Conditions,Proceedings of the 3rd Canada-US Rock Mechanics Symposium,DIEDERICHS Mand GRASSELLI G(Eds.)[C].Toronto,2009,4152.
[8]ZOU S,NADARAJAH N.Optimizing backfill design for ground support and cost saving[A].Golden Rocks 2006,the 41st US Symposium on Rock Mechanics(USRMS),American Rock Mechanics Association[C].Golden:2006:7-21.
[9]LI L.Generalized solution for mining backfill design[J].International Journal of Geomechanics,2014,14(3):04014006.
[10]LI L.Analytical solution for determining the required strength of a side-exposed mine backfill containing a plug[J].Canadian Geotechnical Journal,2014,51(5):508-519.
[11]LI L,AUBETIN M.An improved method to assess the required strength of cemented backfill in underground stopes with an open face[J].International Journal of Mining Science and Technology,2014,24(4):549-558.
[12]LIU G S,LI L,YANG X C,et al.Required strength estimation of a cemented backfill with the front wall exposed and back wall pressured[J].International Journal of Mining and Mineral Engineering,2018,9(1):1-20.
[13]曾照凯,张义平,王永明.高阶段采场充填体强度及稳定性研究[J].金属矿山,2010,(1):31-34.ZENG Zhaokai,ZHANG Yiping,WANG Yongming.Research on the strength and stability on fill body of high-bench stope[J].Metal Mine,2010,(1):31-34.
[14]朱志彬,刘成平.充填体强度计算及稳定性分析[J].采矿技术,2008,8(3):15-17,25.ZHU Zhibin,LIU Chengping.Strength calculation and stability analysis of backfill[J].Mining Technology,2008,8(3):15-17,25.
[15]刘志祥,李夕兵,戴塔根,等.尾砂胶结充填体损伤模型及与岩体的匹配分析[J].岩土力学,2006,27(9):1442-1446.LIU Zhixiang,LI Xibing,DAI Tagen,et al.On damage model of cemented tailings backfill and its match with rock mass[J].Rock and Soil Mechanics,2006,27(9):1442-1446.
[16]刘志祥,李夕兵,赵国彦,等.充填体与岩体三维能量耗损规律及合理匹配[J].岩石力学与工程学报,2010,29(2):344-348.LIU Zhixiang,LI Xibing,ZHAO Guoyan,et al.Three dimensional energy dissipation laws and reasonable matches between backfill and rock mass[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(2):344-348.
[17]LIU Z X,LAN M,XIAO S Y,et al.Damage failure of cemented backfill and its reasonable match with rock mass[J].Transactions of Nonferrous Metals Society of China,2015,25(3):954-959.
[18]刘志祥,李夕兵,张义平.基于混沌优化的高阶段充填体可靠性分析[J].岩土工程学报,2006,28(3):348-352.LIU Zhixiang,LI Xibing,ZHANG Yiping.Reliability analysis of high level backfill based on chaotic optimization[J].Chinese Journal of Geotechnical Engineering,2006,28(3):348-352.
[19]刘志祥,刘青灵,周士霖.基于可靠度理论的充填体强度设计[J].矿冶工程,2012,32(6):1-4,8.LIU Zhixiang,LIU Qingling,ZHOU Shilin.Backfill strength design based on reliability theory[J].Mining and Metallurgical Engineering,2012,32(6):1-4,8.
[20]MARSTON A.The theory of external loads on closed conduits in the light of latest experiments[A].Proceedings of the Ninth Annual Meeting of the Highway Research Board[C].Washington,D.C.:1930,9:138-170.
[21]THOMPSON B,BAWDEN W,GRABINSKY M.In situ measurements of cemented paste backfill at the Cayeli Mine[J].Canadian Geotechnical Journal,2012,49(7):755-772.
[22]EIMKADMI N,AUBERTIN M,LI L.Effect of drainage and sequential filling on the behavior of backfill in mine stopes[J].Canadian Geotechnical Journal,2014,51(1):1-15.
[23]LIU G S,LI L,YANG X C,et al.Numerical analysis of stress distribution in backfilled stopes considering interfaces between the backfill and rock walls[J].International Journal of Geomechanics,2017,17(2):06016014.
[24]LIU G S,LI L,YANG X C,et al.A numerical analysis of the stress distribution in backfilled stopes considering nonplanar interfaces between the backfill and rock walls[J].International Journal of Geotechnical Engineering,2016,10(3):271-282.
[25]LIU G S,LI L,YANG X C,et al.Stability analyses of vertically exposed cemented backfill:A revisit to Mitchell’s physical model tests[J].International Journal of Mining Science and Technology,2016,26(6):1135-1144.
[26]刘钦,李地元,刘志祥,等.水平推力作用下抗滑桩间土拱效应影响因素的数值分析[J].中南大学学报(自然科学版),2011,42(7):2071-2077.LIU Qin,LI Diyuan,LIU Zhixiang,et al.Numerical analysis of influence factors on soil arching effect between anti-sliding piles under horizontal pushing loads[J].Journal of Central South University(Science Edition),2011,42(7):2071-2077.
[27]涂兵雄,贾金青.考虑土拱效应的黏性填土挡土墙主动土压力研究[J].岩石力学与工程学报,2012,31(5):1064-1070.TU Bingxiong,JIA Jinqing.Research on active earth pressure behind rigid retaining wall from clayey backfill considering soil arching effects[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(5):1064-1070.
[28]LI L,AUBERTIN J D,DUBE J S.Stress distribution in a cohesionless backfill poured in a silo[J].Open Civil Engineering Journal,2014,8(1):1-8.
[29]GRABINSKY M W,BAWDEN W F.In situ measurements for geomechanical design of cemented paste backfill systems[A].Proceeding of 9th International Symposium in Mining with Backfill[C].Montreal,2007.
[30]LI L,AUBERTIN M,BELEM T.Formulation of a three dimensional analytical solution to evaluate stresses in backfilled vertical narrow openings[J].Canadian Geotechnical Journal,2005,42(6):1705-1717.
[31]PIRAPAKARAN K,SIVAKUGAN N.Arching within hydraulic fill stopes[J].Geotechnical and Geological Engineering,2007,25(1):25-35.
[32]SOBHI M A,LI L,AUBERTIN M.Numerical investigation of earth pressure coefficient along central line of backfilled stopes[J].Canadian Geotechnical Journal,2017,54(1):138-145.
[33]VEESTRA R.A design procedure for determining the in situ stresses of early age cemented paste backfill[D].Toronto:University of Toronto,Canada,2013.
[34]FALAKNAZ N.Analysis of geomechanical behavior of two adjacent backfilled stopes based on two and three dimensional numerical simulations[D].Montréal:Polytechnique Montreal,Canada,2014.
[35]EMAD M Z.Dynamic performance of cemented rockfill under blastinduced vibrations[D].Montréal:McGill University,2013.
[36]刘光生.充填体与围岩接触成拱作用机理及强度模型研究[D].北京:北京科技大学,2017.LIU Guangsheng.Required strength model of cemented backfill with research on arching mechanism considering backfill-rock interaction[D].Beijing:University of Science and Technology Beijing,2017.
[37]LI L,AUBERTIN M.Numerical investigation of the stress state in inclined backfilled Stopes[J].International Journal of Geomechanics,2009,9(2):52-62.
[38]ASKEW J E,MCCARTHY P L,FITZGERALD D J.Backfill research for pillar extraction at ZC/NBHC[A].Mining with Backfill[C].Sudbury:1978:100-110.
[39]ARIOGLU E.Design aspects of cemented aggregate fill mixes for tungsten stoping operations[J].Mining Science and Technology,1984,1(3):209-214.
[40]LIU G S,LI L,YAO M,et al.An investigation of the uniaxial compressive strength of a cemented hydraulic backfill made of alluvial sand[J].Minerals,2017,7(1):4.