考虑充填顺序与后壁黏结力的采场充填计算统一解
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摘要
以统一强度理论的平面应变抗剪强度公式为基础,合理考虑中间主应力效应、充填顺序、后壁黏结力和顶部超载等综合影响,推导大深宽比采场充填计算时充填料的所需黏聚力统一解和充填体的安全系数统一解,并结合工程算例给出简化公式以及示范计算,继而分析其可比性,最后探讨各因素的影响特性。研究结果表明:本文统一解涵盖了众多的已有解答与新准则解答,具有广泛的理论意义和很好的可比性;2种不同用途的充填计算公式都十分简单,便于实际工程选择及使用;中间主应力效应、充填顺序和后壁黏结力对采场充填计算的影响均很显著,指出现有文献的结果偏于保守,对这3种因素的有效利用可产生重要的经济效益;顶部超载的影响亦不容忽视,应慎重估计顶部超载以实现充填优化计算。
On the basis of the shear strength formulation arising from unified strength theory under plane strain conditions,unified solutions of the required cohesion and the safety factor of the backfill were derived for mine backfills with a high height-to-width ratio. Influencing factors such as the intermediate principal stress effect,the backfilling order and the back wall cohesion as well as the top surcharge were comprehensively considered in the unified solution. The solutions were simplified combining with an engineering case and applied to a specific example. Comparability analysis of the proposed solution was conducted, and parametric studies were also carried out. It was found that the proposed solution contains many conventional and new results and hence, has extensively theoretical value and good comparability. It was also shown that calculation formulas of mine backfills for two different objectives are both easy to use and choose in engineering practice. The influence of the intermediate principal stress effect,the backfilling order and the back wall cohesion on the calculation of mine backfills is significant,and effective usages of these three factors can generate an important economic benefit. Existing results available in the literature are conservative in comparison to the proposed result. The influence of the top surcharge cannot be neglected and should be evaluated for obtaining an optimal calculation of mine backfills.
On the basis of the shear strength formulation arising from unified strength theory under plane strain conditions,unified solutions of the required cohesion and the safety factor of the backfill were derived for mine backfills with a high height-to-width ratio. Influencing factors such as the intermediate principal stress effect,the backfilling order and the back wall cohesion as well as the top surcharge were comprehensively considered in the unified solution. The solutions were simplified combining with an engineering case and applied to a specific example. Comparability analysis of the proposed solution was conducted, and parametric studies were also carried out. It was found that the proposed solution contains many conventional and new results and hence, has extensively theoretical value and good comparability. It was also shown that calculation formulas of mine backfills for two different objectives are both easy to use and choose in engineering practice. The influence of the intermediate principal stress effect,the backfilling order and the back wall cohesion on the calculation of mine backfills is significant,and effective usages of these three factors can generate an important economic benefit. Existing results available in the literature are conservative in comparison to the proposed result. The influence of the top surcharge cannot be neglected and should be evaluated for obtaining an optimal calculation of mine backfills.
引文
[1]吴爱祥,王勇,王洪江.膏体充填技术现状及趋势[J].金属矿山,2016,(7):1-9.(WU Aixiang,WANG Yong,WANG Hongjiang.Status and prospects of the paste backfill technology[J].Metal Mine,2016,(7):1-9.(in Chinese))
[2]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.
[3]LI L,AUBERTIN M.A modified solution to assess the required strength of exposed backfill in mine stopes[J].Canadian Geotechnical Journal,2012,49(8):994-1 002.
[4]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.
[5]张洪岩,穆磊,刘承磊.基于FLAC3D的地下采场充填体内部拱效应的数值模拟研究[J].中国水运,2016,16(1):111-112.(ZHANG Hongyan,MU Lei,LIU Chenglei.Study on numerical simulation of FLAC3D underground stope backfill based on internal arching effect[J].China Water Transport,2016,16(1):111-112.(in Chinese))
[6]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):648-654.(WUAixiang,SHEN Huiming,JIANG Lichun,et al.Arching effect of long-narrow cemented paste backfill body and its effect on target strength[J].The Chinese Journal of Nonferrous Metals,2016,26(3):648-654.(in Chinese))
[7]马小龙.矿山采场回填的应力拱效应数值分析[J].西部探矿工程,2016,28(3):100-102.(MA Xiaolong.Numerical analysis of the stress arch effect in mine stope backfill[J].West-China Exploration Engineering,2016,28(3):100-102.(in Chinese))
[8]杨磊,邱景平,邢军,等.高窄型充填采场内的拱效应及应力分布状态研究[J].中国安全生产科学技术,2016,12(7):22-26.(YANG Lei,QIU Jingping,XING Jun,et al.Study on arching effect and stress distribution state in high-narrow filling stope[J].Journal of Safety Science and Technology,2016,12(7):22-26.(in Chinese))
[9]耿智园,杨磊,邱景平.拱效应对狭窄型充填采场内应力分布状态的影响[J].金属矿山,2017,(1):16-19.(GENG Zhiyuan,YANGLei,QIU Jingping.Influence of arching effect on stress distribution in narrow backfilled stopes[J].Metal Mine,2017,(1):16-19.(in Chinese))
[10]LADE P V.Assessment of test data for selection of 3-D failure criterion for sand[J].International Journal for Numerical and Analytical Methods in Geomechanics,2006,30(4):307-333.
[11]MATSUOKA H,SUN D A,KOGANE A,et al.Stress-strain behaviour of unsaturated soil in true triaxial tests[J].Canadian Geotechnical Journal,2002,39(3):608-619.
[12]于清高,邵生俊,佘芳涛,等.真三轴条件下Q2黄土的破坏模式与强度特性研究[J].岩土力学,2010,31(1):66-70.(YU Qinggao,SHAO Shengjun,SHE Fangtao,et al.Research on failure modes and strength characteristics of Q2 loess under true triaxial condition[J].Rock and Soil Mechanics,2010,31(1):66-70.(in Chinese))
[13]NANDA S,PATRA N R.Determination of soil properties for plane strain condition from the triaxial tests results[J].International Journal for Numerical and Analytical Methods in Geomechanics,2015,39(9):1 014-1 026.
[14]DUAN K,KWOK C Y,MA X D.DEM simulations of sandstone under true triaxial compressive tests[J].Acta Geotechnica,2017,12(3):495-510.
[15]俞茂宏.岩土类材料的统一强度理论及其应用[J].岩土工程学报,1994,16(2):1-10.(YU Maohong.Unified strength theory of geomaterials and its application[J].Chinese Journal of Geotechnical Engineering,1994,16(2):1-10.(in Chinese))
[16]俞茂宏.双剪理论及其应用[M].北京:科学出版社,1998:249-288.(YU Maohong.Twin-shear theory and its application[M].Beijing:Science Press,1998:249-288.(in Chinese))
[17]张常光,张庆贺,赵均海.非饱和土抗剪强度及土压力统一解[J].岩土力学,2010,31(6):1 871-1 876.(ZHANG Changguang,ZHANG Qinghe,ZHAO Junhai.Unified solutions of shear strength and earth pressure for unsaturated soils[J].Rock and Soil Mechanics,2010,31(6):1 871-1 876.(in Chinese))
[18]赵春风,杨砚宗,张常光,等.考虑中主应力的常用破坏准则适用性研究[J].岩石力学与工程学报,2011,30(2):327-334.(ZHAOChunfeng,YANG Yanzong,ZHANG Changguang,et al.Investigation on applicability of common failure criteria considering intermediate principal stress[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(2):327-334.(in Chinese))
[19]张常光,赵均海,杜文超.岩石中间主应力效应及强度理论研究进展[J].建筑科学与工程学报,2014,31(2):6-19.(ZHANGChangguang,ZHAO Junhai,DU Wenchao.Advances in rock for intermediate principal stress effect and strength theory[J].Journal of Architecture and Civil Engineering,2014,31(2):6-19.(in Chinese))
[20]张常光,范文,赵均海.非饱和土统一强度理论及真三轴试验结果验证[J].岩石力学与工程学报,2015,34(8):1 702-1 711.(ZHANG Changguang,FAN Wen,ZHAO Junhai.Unified strength theory of unsaturated soils and verification with true triaxial test[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(8):1 702-1 711.(in Chinese))
[21]黄亚娟,赵均海,田文秀.基于双剪统一强度理论的刚性结构物竖直土压力计算[J].建筑科学与工程学报,2008,25(1):107-110.(HUANG Yajuan,ZHAO Junhai,TIAN Wenxiu.Calculation of vertical earth pressure of rigidity structures based on two shear unified strength theory[J].Journal of Architecture and Civil Engineering,2008,25(1):107-110.(in Chinese))
[22]赵春风,杨砚宗,张常光,等.考虑中间主应力与剪胀的新邓肯-张模型[J].同济大学学报:自然科学版,2011,39(3):309-313.(ZHAO Chunfeng,YANG Yanzong,ZHANG Changguang,et al.An improved Duncan-Chang model considering effects of intermediate principal stress and shear dilatancy[J].Journal of Tongji University:Natural Science,2011,39(3):309-313.(in Chinese))
[23]ZHANG C G,ZHAO J H,ZHANG Q H,et al.A new closed-form solution for circular openings modeled by the unified strength theory and radius-dependent Young′s modulus[J].Computers and Geotechnics,2012,42:118-128.
[24]MA Z Y,LIAO H J,DANG F N.Influence of intermediate principal stress on the bearing capacity of strip and circular footings[J].Journal of Engineering Mechanics,2014,140(7):04014041.
[25]张常光,范文,赵均海.深埋圆形巷道围岩塑性区位移及特征曲线新解和参数分析[J].岩土力学,2016,37(1):12-24.(ZHANGChangguang,FAN Wen,ZHAO Junhai.New solutions of rock plastic displacement and ground response curve for a deep circular tunnel and parametric analysis[J].Rock and Soil Mechanics,2016,37(1):12-24.(in Chinese))
[26]张常光,晏青,张成林.考虑中间主应力的路堤临界填土高度统一解及比较[J].岩石力学与工程学报,2016,35(7):1 466-1 473.(ZHANG Changguang,YAN Qing,ZHANG Chenglin.A unified solution of critical filling height for embankment considering intermediate principal stress and its comparisons[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(7):1 466-1 473.(in Chinese))
[27]尹万蕾,潘一山,李忠华.考虑塑性区强度参数劣化的圆形巷道冲击地压临界条件研究[J].煤炭学报,2018,43(2):348-355.(YINWanlei,PAN Yishan,LI Zhonghua.Critical condition of rock burst in the circular tunnel based on the strength parameters of the degradation in the plastic zone[J].Journal of China Coal Society,2018,43(2):348-355.(in Chinese))
[28]LI L,DUBéJ,ZANGENEHMADAR Z.Estimation of total and effective stresses in trenches with inclined walls[J].International Journal of Geotechnical Engineering,2012,6(4):525-538.
[2]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.
[3]LI L,AUBERTIN M.A modified solution to assess the required strength of exposed backfill in mine stopes[J].Canadian Geotechnical Journal,2012,49(8):994-1 002.
[4]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.
[5]张洪岩,穆磊,刘承磊.基于FLAC3D的地下采场充填体内部拱效应的数值模拟研究[J].中国水运,2016,16(1):111-112.(ZHANG Hongyan,MU Lei,LIU Chenglei.Study on numerical simulation of FLAC3D underground stope backfill based on internal arching effect[J].China Water Transport,2016,16(1):111-112.(in Chinese))
[6]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):648-654.(WUAixiang,SHEN Huiming,JIANG Lichun,et al.Arching effect of long-narrow cemented paste backfill body and its effect on target strength[J].The Chinese Journal of Nonferrous Metals,2016,26(3):648-654.(in Chinese))
[7]马小龙.矿山采场回填的应力拱效应数值分析[J].西部探矿工程,2016,28(3):100-102.(MA Xiaolong.Numerical analysis of the stress arch effect in mine stope backfill[J].West-China Exploration Engineering,2016,28(3):100-102.(in Chinese))
[8]杨磊,邱景平,邢军,等.高窄型充填采场内的拱效应及应力分布状态研究[J].中国安全生产科学技术,2016,12(7):22-26.(YANG Lei,QIU Jingping,XING Jun,et al.Study on arching effect and stress distribution state in high-narrow filling stope[J].Journal of Safety Science and Technology,2016,12(7):22-26.(in Chinese))
[9]耿智园,杨磊,邱景平.拱效应对狭窄型充填采场内应力分布状态的影响[J].金属矿山,2017,(1):16-19.(GENG Zhiyuan,YANGLei,QIU Jingping.Influence of arching effect on stress distribution in narrow backfilled stopes[J].Metal Mine,2017,(1):16-19.(in Chinese))
[10]LADE P V.Assessment of test data for selection of 3-D failure criterion for sand[J].International Journal for Numerical and Analytical Methods in Geomechanics,2006,30(4):307-333.
[11]MATSUOKA H,SUN D A,KOGANE A,et al.Stress-strain behaviour of unsaturated soil in true triaxial tests[J].Canadian Geotechnical Journal,2002,39(3):608-619.
[12]于清高,邵生俊,佘芳涛,等.真三轴条件下Q2黄土的破坏模式与强度特性研究[J].岩土力学,2010,31(1):66-70.(YU Qinggao,SHAO Shengjun,SHE Fangtao,et al.Research on failure modes and strength characteristics of Q2 loess under true triaxial condition[J].Rock and Soil Mechanics,2010,31(1):66-70.(in Chinese))
[13]NANDA S,PATRA N R.Determination of soil properties for plane strain condition from the triaxial tests results[J].International Journal for Numerical and Analytical Methods in Geomechanics,2015,39(9):1 014-1 026.
[14]DUAN K,KWOK C Y,MA X D.DEM simulations of sandstone under true triaxial compressive tests[J].Acta Geotechnica,2017,12(3):495-510.
[15]俞茂宏.岩土类材料的统一强度理论及其应用[J].岩土工程学报,1994,16(2):1-10.(YU Maohong.Unified strength theory of geomaterials and its application[J].Chinese Journal of Geotechnical Engineering,1994,16(2):1-10.(in Chinese))
[16]俞茂宏.双剪理论及其应用[M].北京:科学出版社,1998:249-288.(YU Maohong.Twin-shear theory and its application[M].Beijing:Science Press,1998:249-288.(in Chinese))
[17]张常光,张庆贺,赵均海.非饱和土抗剪强度及土压力统一解[J].岩土力学,2010,31(6):1 871-1 876.(ZHANG Changguang,ZHANG Qinghe,ZHAO Junhai.Unified solutions of shear strength and earth pressure for unsaturated soils[J].Rock and Soil Mechanics,2010,31(6):1 871-1 876.(in Chinese))
[18]赵春风,杨砚宗,张常光,等.考虑中主应力的常用破坏准则适用性研究[J].岩石力学与工程学报,2011,30(2):327-334.(ZHAOChunfeng,YANG Yanzong,ZHANG Changguang,et al.Investigation on applicability of common failure criteria considering intermediate principal stress[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(2):327-334.(in Chinese))
[19]张常光,赵均海,杜文超.岩石中间主应力效应及强度理论研究进展[J].建筑科学与工程学报,2014,31(2):6-19.(ZHANGChangguang,ZHAO Junhai,DU Wenchao.Advances in rock for intermediate principal stress effect and strength theory[J].Journal of Architecture and Civil Engineering,2014,31(2):6-19.(in Chinese))
[20]张常光,范文,赵均海.非饱和土统一强度理论及真三轴试验结果验证[J].岩石力学与工程学报,2015,34(8):1 702-1 711.(ZHANG Changguang,FAN Wen,ZHAO Junhai.Unified strength theory of unsaturated soils and verification with true triaxial test[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(8):1 702-1 711.(in Chinese))
[21]黄亚娟,赵均海,田文秀.基于双剪统一强度理论的刚性结构物竖直土压力计算[J].建筑科学与工程学报,2008,25(1):107-110.(HUANG Yajuan,ZHAO Junhai,TIAN Wenxiu.Calculation of vertical earth pressure of rigidity structures based on two shear unified strength theory[J].Journal of Architecture and Civil Engineering,2008,25(1):107-110.(in Chinese))
[22]赵春风,杨砚宗,张常光,等.考虑中间主应力与剪胀的新邓肯-张模型[J].同济大学学报:自然科学版,2011,39(3):309-313.(ZHAO Chunfeng,YANG Yanzong,ZHANG Changguang,et al.An improved Duncan-Chang model considering effects of intermediate principal stress and shear dilatancy[J].Journal of Tongji University:Natural Science,2011,39(3):309-313.(in Chinese))
[23]ZHANG C G,ZHAO J H,ZHANG Q H,et al.A new closed-form solution for circular openings modeled by the unified strength theory and radius-dependent Young′s modulus[J].Computers and Geotechnics,2012,42:118-128.
[24]MA Z Y,LIAO H J,DANG F N.Influence of intermediate principal stress on the bearing capacity of strip and circular footings[J].Journal of Engineering Mechanics,2014,140(7):04014041.
[25]张常光,范文,赵均海.深埋圆形巷道围岩塑性区位移及特征曲线新解和参数分析[J].岩土力学,2016,37(1):12-24.(ZHANGChangguang,FAN Wen,ZHAO Junhai.New solutions of rock plastic displacement and ground response curve for a deep circular tunnel and parametric analysis[J].Rock and Soil Mechanics,2016,37(1):12-24.(in Chinese))
[26]张常光,晏青,张成林.考虑中间主应力的路堤临界填土高度统一解及比较[J].岩石力学与工程学报,2016,35(7):1 466-1 473.(ZHANG Changguang,YAN Qing,ZHANG Chenglin.A unified solution of critical filling height for embankment considering intermediate principal stress and its comparisons[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(7):1 466-1 473.(in Chinese))
[27]尹万蕾,潘一山,李忠华.考虑塑性区强度参数劣化的圆形巷道冲击地压临界条件研究[J].煤炭学报,2018,43(2):348-355.(YINWanlei,PAN Yishan,LI Zhonghua.Critical condition of rock burst in the circular tunnel based on the strength parameters of the degradation in the plastic zone[J].Journal of China Coal Society,2018,43(2):348-355.(in Chinese))
[28]LI L,DUBéJ,ZANGENEHMADAR Z.Estimation of total and effective stresses in trenches with inclined walls[J].International Journal of Geotechnical Engineering,2012,6(4):525-538.