考虑剪胀与中间主应力的被锚巷道围岩稳定性分析
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摘要
为研究被锚巷道围岩稳定性,将锚杆的支护作用考虑成作用于锚固体两侧的一组夹紧力与强化了锚固体强度参数,综合考虑围岩剪胀特性与中间主应力效应,建立被锚圆巷弹塑性力学模型,推导出围岩的应力场与位移场解析解,求得围岩塑性区半径表达式。算例研究表明:随着中间主应力系数增大,塑性区半径、洞壁位移与锚杆轴力均减小,最大主应力峰值增大;随着剪胀角增大,塑性区半径稍有减小,最大主应力峰值稍有增大,洞壁位移与锚杆轴力急剧增大;影响因素最不利组合(b=0,ψ=30°)与影响因素最有利组合(b=1,ψ=0°)相比,塑性区半径增大了23.49%,最大主应力峰值变化很小,洞壁位移增大了76.20%,锚杆轴力增大了1.94倍。该结果在围岩稳定分析方面具有一定工程实用价值,也可为锚杆支护设计和优化提供一定理论基础。
To study the surrounding rock stability of bolted roadway, the supporting effect of the bolt is considered as a set of clamping forces acting on both sides of the anchor bolt, and the strength parameters of the anchor bolt are strengthened. With the dilatancy characteristics and intermediate principal stress effects of the surrounding rock comprehensively considered, an elasto-plastic mechanical model of the bolted circular roadway is established, and the analytical solutions to the stress field and displacement field of the surrounding rock are derived, and the expression of the radius of the surrounding rock plastic zone is obtained. The results have shown that with the increase of the intermediate principal stress coefficient, the radius of the plastic zone, the displacement of the cave wall and the axial force of the bolt all decrease, but the peak value of the maximum principal stress increases. As the dilatancy angle increases, the radius of the plastic zone decreases slightly and the peak value of the maximum principal stress increases slightly, but the displacement of the roadway cavern wall and the axial force of the bolt increase sharply. With the most unfavorable combination of the impact factors(b=1, ψ=0°) compared against the most favorable combination of the impact factors(b=0, ψ=30°), the radius of the plastic zone increases by 23.49%, the peak of maximum principal stress changes slightly, the wall displacement increases by 76.20%, and the axial force of the bolt increases by 1.94 times. The results have certain engineering practical value in the stability analysis of the surrounding rock, and also provide certain theoretical basis for the design and optimization of bolt support.
To study the surrounding rock stability of bolted roadway, the supporting effect of the bolt is considered as a set of clamping forces acting on both sides of the anchor bolt, and the strength parameters of the anchor bolt are strengthened. With the dilatancy characteristics and intermediate principal stress effects of the surrounding rock comprehensively considered, an elasto-plastic mechanical model of the bolted circular roadway is established, and the analytical solutions to the stress field and displacement field of the surrounding rock are derived, and the expression of the radius of the surrounding rock plastic zone is obtained. The results have shown that with the increase of the intermediate principal stress coefficient, the radius of the plastic zone, the displacement of the cave wall and the axial force of the bolt all decrease, but the peak value of the maximum principal stress increases. As the dilatancy angle increases, the radius of the plastic zone decreases slightly and the peak value of the maximum principal stress increases slightly, but the displacement of the roadway cavern wall and the axial force of the bolt increase sharply. With the most unfavorable combination of the impact factors(b=1, ψ=0°) compared against the most favorable combination of the impact factors(b=0, ψ=30°), the radius of the plastic zone increases by 23.49%, the peak of maximum principal stress changes slightly, the wall displacement increases by 76.20%, and the axial force of the bolt increases by 1.94 times. The results have certain engineering practical value in the stability analysis of the surrounding rock, and also provide certain theoretical basis for the design and optimization of bolt support.
引文
[1]蔡海兵,程桦,荣传新.基于广义Hoek-Brown准则的深埋硐室围岩塑性区位移分析[J].采矿与安全工程学报,2015,32(5):778-785.CAI Haibing,CHENG Hua,RONG Chuanxin.Analysis on rock plastic zone displacement of deep buried underground chamber based on generalized Hoek-Brown criterion[J].Journal of Mining&Safety Engineering,2015,32(5):778-785.
[2]张强,王水林,葛修润.圆形巷道围岩应变软化弹塑性分析[J].岩石力学与工程学报,2010,29(5):1031-1035.ZHANG Qiang,WANG Shuilin,GE Xiurun.Elastoplastic analysis of circular openings in strainsoftening rock masses[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(5):1031-1035.
[3]文竞舟,张永兴,王成.隧道围岩全长黏结式锚杆界面力学模型研究[J].岩土力学,2013,34(6):1645-1651.WEN Jingzhou,ZHANG Yongxing,WANG Cheng.Study of mechanical model of fully grouted rock bolt’s anchorage interface in tunnel surrounding rock[J].Rock and Soil Mechanics,2013,34(6):1645-1651.
[4]侯公羽,牛晓松.基于Levy-Mises本构关系及Hoek-Brown屈服准则的轴对称圆巷理想弹塑性解[J].岩石力学与工程学报,2010,29(4):765-777.HOU Gongyu,NIU Xiaosong.Perfect elastoplatic solution of axisymmetric cylindrical cavity based on Levy-Mises constitutive relation and Hoek-Brown failure criterion[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(4):765-777.
[5]温森,杨圣奇.基于Hoek-Brown准则的隧洞围岩变形研究[J].岩土力学,2011,32(1):63-69.WEN Sen,YANG Shengqi.Study of deformations of surrounding rock of tunnel based on Hoek-Brown criterion[J].Rock and Soil Mechanics,2011,32(1):63-69.
[6]张强,王红英,王水林,等.基于统一强度理论的破裂围岩劣化弹塑性分析[J].煤炭学报,2010,35(3):381-386.ZHANG Qiang,WANG Hongying,WANG Shuilin,et al.Deterioration elasto-plastic analysis of cracked surrounding rocks based on unified strength theory[J].Journal of China Coal Society,2010,35(3):381-386.
[7]YU M H,XIA G Y,KOLUPAEY V A.Basic characteristics and development of yield criteria for geomaterials[J].Journal of Rock Mechanics and Geotechnical Engineering,2009,1(1):71-78.
[8]范文,俞茂宏,陈立伟,等.考虑剪胀及软化的洞室围岩弹塑性分析的统一解[J].岩石力学与工程学报,2004,23(19):3213-3220.FAN Wen,YU Maohong,CHEN Liwei,et al.Unified elastoplastic solution for surrounding rocks of openings with consideration of material dilatancy and softening[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(19):3213-3220.
[9]曾开华,鞠海燕,盛国君,等.巷道围岩弹塑性解析解及工程应用[J].煤炭学报,2011,36(5):752-755.ZENG Kaihua,JU Haiyan,SHENG Guojun,et al.Elastic-plastic analytical solutions for surrounding rocks of tunnels and its engineering applications[J].Journal of China Coal Society,2011,36(5):752-755.
[10]张小波,赵光明,孟祥瑞.考虑峰后应变软化与扩容的圆形巷道围岩弹塑性D-P准则解[J].采矿与安全工程学报,2013,30(6):903-910,916.ZHANG Xiaobo,ZHAO Guangming,MENG Xiangrui.Elastoplastic solution for surrounding rock of circular roadway based on D-P criterion by considering post-peak strain softening and dilatancy[J].Journal of Mining&Safety Engineering,2013,30(6):903-910,916.
[11]赵星光,蔡明,蔡美峰.剪胀对地下工程岩体位移的影响:以加拿大Donkin-Morie隧道为例[J].岩石力学与工程学报,2010,29(11):2185-2195.ZHAO Xingguang,CAI Ming,CAI Meifeng.Influence of dilation on rock mass displacement around underground excavations:a case study of Donkin-Morien tunnel in Canada[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(11):2185-2195.
[12]陈梁,茅献彪,李明,等.基于Drucker-Prager准则的深部巷道破裂围岩弹塑性分析[J].煤炭学报,2017,42(2):484-491.CHEN Liang,MAO Xianbiao,LI Ming,et al.Elastoplastic analysis of cracked surrounding rock in deep roadway based on Drucker-Prager criterion[J].Journal of China Coal Society,2017,42(2):484-491.
[13]余东明,范永丰,段建新,等.考虑中间主应力的深埋圆形隧道弹塑性统一解[J].上海交通大学学报,2013,47(9):1447-1453.YU Dongming,FAN Yongfeng,DUAN Jianxin,et al.Elastoplastic unified solutions to deep-buried circular tunnels considering intermediate principal stress[J].Journal of Shanghai Jiao Tong University,2013,47(9):1447-1453.
[14]刘志钦,余东明.考虑中间主应力和剪胀特性的深埋圆巷弹塑性应力位移解[J].工程力学,2012,29(8):289-296.LIU Zhiqin,YU Dongming.Elastoplastic stress and displacement analytical solutions to deep-buried circular tunnels considering intermediate principal stress and dilatancy[J].Engineering Mechanics,2012,29(8):289-296.
[15]潘继良,高召宁,郑志伟,等.考虑损伤与剪胀及中间主应力的巷道围岩弹塑性分析[J].中国安全生产科学技术,2017,13(2):40-45.PAN Jiliang,GAO Zhaoning,ZHENG Zhiwei,et al.Elasto-plastic analysis on surrounding rock of roadway considering damage,shear dilation and intermediate principal stress[J].Journal of Safety Science and Technology,2017,13(2):40-45.
[16]侯公羽,李晶晶,杨悦,等.围岩弹塑性变形条件下锚杆、喷混凝土和U型钢的支护效果研究[J].岩土力学,2014,35(5):1357-1376.HOU Gongyu,LI Jingjing,YANG Yue,et al.Support effects of anchor bolt,shotcrete and U-steel in elastoplastic stage of surrounding rock[J].Rock and Soil Mechanics,2014,35(5):1357-1376.
[17]崔芳,高永涛,吴顺川.轴对称荷载作用下圆形隧道围岩变形解析[J].北京科技大学学报,2011,33(11):1043-1047.CUI Fang,GAO Yongtao,WU Shunchuan.Analytic solutions for surrounding rock mass deformation of circular tunnels subjected to axisymmetric loads[J].Journal of University of Science and Technology Beijing,2011,33(11):1043-1047.
[18]PELIZZA S,KIM S H,KIM J S.A study of strength parameters in the reinforced ground by rock bolts[C]//Seoul:Proceedings of the World Tunnel Congress and32nd ITA Assembly,2006:06-0385.
[19]杨双锁,张百胜.锚杆对岩土体作用的力学本质[J].岩土力学,2003,24(10):280-282.YANG Shuangsuo,ZHANG Baisheng.The influence of bolt action force to the mechanical property of rocks[J].Rock and Soil Mechanics,2003,24(10):280-282.
[20]李大伟,侯朝炯.巷道锚杆支护特性分析与应用[J].煤炭学报,2008,33(6):613-618.LI Dawei,HOU Chaojiong.Analysis and application on bolt support characteristic of roadway[J].Journal of China Coal Society,2008,33(6):613-618.
[21]侯朝炯.深部巷道围岩控制的关键技术研究[J].中国矿业大学学报,2017,46(5):972-976.HOU Chaojiong.Key technologies for surrounding rock control in deep roadway[J].Journal of China University of Mining&Technology,2017,46(5):972-976.
[22]范浩,刘万荣,付腾飞,等.考虑渗流剪胀和中间主应力的隧洞围岩稳定性分析[J].中国安全科学学报,2016,26(2):139-145.FAN Hao,LIU Wanrong,FU Tengfei,et al.Stability analysis of surrounding rock of tunnel considering seepage,shear dilation and intermediate principal stress[J].China Safety Science Journal,2016,26(2):139-145.
[23]张斌伟,严松宏,李平.考虑围岩非线性和剪胀特性的地下硐室极限解[J].地下空间与工程学报,2012,8(3):473-479.ZHANG Binwei,YAN Songhong,LI Ping.Limit solution of underground chamber considering non-linear softening and dilatancy of surrounding rock[J].Chinese Journal of Underground Space and Engineering,2012,8(3):473-479.
[2]张强,王水林,葛修润.圆形巷道围岩应变软化弹塑性分析[J].岩石力学与工程学报,2010,29(5):1031-1035.ZHANG Qiang,WANG Shuilin,GE Xiurun.Elastoplastic analysis of circular openings in strainsoftening rock masses[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(5):1031-1035.
[3]文竞舟,张永兴,王成.隧道围岩全长黏结式锚杆界面力学模型研究[J].岩土力学,2013,34(6):1645-1651.WEN Jingzhou,ZHANG Yongxing,WANG Cheng.Study of mechanical model of fully grouted rock bolt’s anchorage interface in tunnel surrounding rock[J].Rock and Soil Mechanics,2013,34(6):1645-1651.
[4]侯公羽,牛晓松.基于Levy-Mises本构关系及Hoek-Brown屈服准则的轴对称圆巷理想弹塑性解[J].岩石力学与工程学报,2010,29(4):765-777.HOU Gongyu,NIU Xiaosong.Perfect elastoplatic solution of axisymmetric cylindrical cavity based on Levy-Mises constitutive relation and Hoek-Brown failure criterion[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(4):765-777.
[5]温森,杨圣奇.基于Hoek-Brown准则的隧洞围岩变形研究[J].岩土力学,2011,32(1):63-69.WEN Sen,YANG Shengqi.Study of deformations of surrounding rock of tunnel based on Hoek-Brown criterion[J].Rock and Soil Mechanics,2011,32(1):63-69.
[6]张强,王红英,王水林,等.基于统一强度理论的破裂围岩劣化弹塑性分析[J].煤炭学报,2010,35(3):381-386.ZHANG Qiang,WANG Hongying,WANG Shuilin,et al.Deterioration elasto-plastic analysis of cracked surrounding rocks based on unified strength theory[J].Journal of China Coal Society,2010,35(3):381-386.
[7]YU M H,XIA G Y,KOLUPAEY V A.Basic characteristics and development of yield criteria for geomaterials[J].Journal of Rock Mechanics and Geotechnical Engineering,2009,1(1):71-78.
[8]范文,俞茂宏,陈立伟,等.考虑剪胀及软化的洞室围岩弹塑性分析的统一解[J].岩石力学与工程学报,2004,23(19):3213-3220.FAN Wen,YU Maohong,CHEN Liwei,et al.Unified elastoplastic solution for surrounding rocks of openings with consideration of material dilatancy and softening[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(19):3213-3220.
[9]曾开华,鞠海燕,盛国君,等.巷道围岩弹塑性解析解及工程应用[J].煤炭学报,2011,36(5):752-755.ZENG Kaihua,JU Haiyan,SHENG Guojun,et al.Elastic-plastic analytical solutions for surrounding rocks of tunnels and its engineering applications[J].Journal of China Coal Society,2011,36(5):752-755.
[10]张小波,赵光明,孟祥瑞.考虑峰后应变软化与扩容的圆形巷道围岩弹塑性D-P准则解[J].采矿与安全工程学报,2013,30(6):903-910,916.ZHANG Xiaobo,ZHAO Guangming,MENG Xiangrui.Elastoplastic solution for surrounding rock of circular roadway based on D-P criterion by considering post-peak strain softening and dilatancy[J].Journal of Mining&Safety Engineering,2013,30(6):903-910,916.
[11]赵星光,蔡明,蔡美峰.剪胀对地下工程岩体位移的影响:以加拿大Donkin-Morie隧道为例[J].岩石力学与工程学报,2010,29(11):2185-2195.ZHAO Xingguang,CAI Ming,CAI Meifeng.Influence of dilation on rock mass displacement around underground excavations:a case study of Donkin-Morien tunnel in Canada[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(11):2185-2195.
[12]陈梁,茅献彪,李明,等.基于Drucker-Prager准则的深部巷道破裂围岩弹塑性分析[J].煤炭学报,2017,42(2):484-491.CHEN Liang,MAO Xianbiao,LI Ming,et al.Elastoplastic analysis of cracked surrounding rock in deep roadway based on Drucker-Prager criterion[J].Journal of China Coal Society,2017,42(2):484-491.
[13]余东明,范永丰,段建新,等.考虑中间主应力的深埋圆形隧道弹塑性统一解[J].上海交通大学学报,2013,47(9):1447-1453.YU Dongming,FAN Yongfeng,DUAN Jianxin,et al.Elastoplastic unified solutions to deep-buried circular tunnels considering intermediate principal stress[J].Journal of Shanghai Jiao Tong University,2013,47(9):1447-1453.
[14]刘志钦,余东明.考虑中间主应力和剪胀特性的深埋圆巷弹塑性应力位移解[J].工程力学,2012,29(8):289-296.LIU Zhiqin,YU Dongming.Elastoplastic stress and displacement analytical solutions to deep-buried circular tunnels considering intermediate principal stress and dilatancy[J].Engineering Mechanics,2012,29(8):289-296.
[15]潘继良,高召宁,郑志伟,等.考虑损伤与剪胀及中间主应力的巷道围岩弹塑性分析[J].中国安全生产科学技术,2017,13(2):40-45.PAN Jiliang,GAO Zhaoning,ZHENG Zhiwei,et al.Elasto-plastic analysis on surrounding rock of roadway considering damage,shear dilation and intermediate principal stress[J].Journal of Safety Science and Technology,2017,13(2):40-45.
[16]侯公羽,李晶晶,杨悦,等.围岩弹塑性变形条件下锚杆、喷混凝土和U型钢的支护效果研究[J].岩土力学,2014,35(5):1357-1376.HOU Gongyu,LI Jingjing,YANG Yue,et al.Support effects of anchor bolt,shotcrete and U-steel in elastoplastic stage of surrounding rock[J].Rock and Soil Mechanics,2014,35(5):1357-1376.
[17]崔芳,高永涛,吴顺川.轴对称荷载作用下圆形隧道围岩变形解析[J].北京科技大学学报,2011,33(11):1043-1047.CUI Fang,GAO Yongtao,WU Shunchuan.Analytic solutions for surrounding rock mass deformation of circular tunnels subjected to axisymmetric loads[J].Journal of University of Science and Technology Beijing,2011,33(11):1043-1047.
[18]PELIZZA S,KIM S H,KIM J S.A study of strength parameters in the reinforced ground by rock bolts[C]//Seoul:Proceedings of the World Tunnel Congress and32nd ITA Assembly,2006:06-0385.
[19]杨双锁,张百胜.锚杆对岩土体作用的力学本质[J].岩土力学,2003,24(10):280-282.YANG Shuangsuo,ZHANG Baisheng.The influence of bolt action force to the mechanical property of rocks[J].Rock and Soil Mechanics,2003,24(10):280-282.
[20]李大伟,侯朝炯.巷道锚杆支护特性分析与应用[J].煤炭学报,2008,33(6):613-618.LI Dawei,HOU Chaojiong.Analysis and application on bolt support characteristic of roadway[J].Journal of China Coal Society,2008,33(6):613-618.
[21]侯朝炯.深部巷道围岩控制的关键技术研究[J].中国矿业大学学报,2017,46(5):972-976.HOU Chaojiong.Key technologies for surrounding rock control in deep roadway[J].Journal of China University of Mining&Technology,2017,46(5):972-976.
[22]范浩,刘万荣,付腾飞,等.考虑渗流剪胀和中间主应力的隧洞围岩稳定性分析[J].中国安全科学学报,2016,26(2):139-145.FAN Hao,LIU Wanrong,FU Tengfei,et al.Stability analysis of surrounding rock of tunnel considering seepage,shear dilation and intermediate principal stress[J].China Safety Science Journal,2016,26(2):139-145.
[23]张斌伟,严松宏,李平.考虑围岩非线性和剪胀特性的地下硐室极限解[J].地下空间与工程学报,2012,8(3):473-479.ZHANG Binwei,YAN Songhong,LI Ping.Limit solution of underground chamber considering non-linear softening and dilatancy of surrounding rock[J].Chinese Journal of Underground Space and Engineering,2012,8(3):473-479.
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