非等压圆形巷道围岩塑性区边界方程及应用
|
摘要
由于双向非等压应力条件作用下的圆形巷道弹塑性问题求解难度较大,目前难以得到精确解析解。基于Mohr-Coulomb强度准则,将Kirsch解代入塑性条件中研究了非等压应力条件下圆形巷道围岩塑性区近似边界方程、分析了塑性区影响因素及形成力学机制。结果表明:侧压系数影响塑性区形态,原岩应力方向影响蝶形塑性区蝶叶方位,巷道半径与围岩岩性对塑性区形态均没有影响,但对塑性区的发育深度起着决定作用;侧压系数不等于1时,最大主应力方向不再平行于巷道切向,最小主应力方向不再经过巷道中心位置,引起围岩剪切破坏方向发生变化,而塑性区的扩展受控于最大剪应力的分布,此时塑性区形态偏离圆形;剪应力峰值点曲线与塑性区边界均随侧压系数变化而发生变化,但塑性区边界总是位于剪应力云图中最大剪应力峰值位置,且侧压系数越小主应力方向变化越大,塑性区不规则形态越明显;该求解方法没有考虑塑性区对弹性区应力的影响,属于近似求解法,但塑性区形态、发育规律与数值模拟结果相一致,并对解决工程问题具有指导作用,说明该塑性区边界方程近似解法是可信的。通过该近似方程能够掌握巷道围岩塑性区发育扩展规律,依此提出的可接长锚杆支护技术能够有效解决深部巷道锚杆易随顶板整体下沉、锚索破断引发的冒顶问题,较好的消除了冒顶隐患。
At present,it is difficult to obtain the exact analytical solution of elastic-plastic problem of circular roadway under bidirectional non-axisymmetric stress. Based on Mohr-Coulomb strength criterion,the approximate boundary equation of plastic zone is studied by substituting Kirsch equation into plastic condition. Also,the influencing factors and mechanics mechanism of formation of plastic zone are analyzed. The results show that the lateral pressure coefficient affects the shape of plastic zone,the direction of in-situ stresses affects the position of butterfly leaf of butterflyshaped plastic zone,and the radius and lithology of roadway affect the radius of plastic zone.When the value of lateral pressure coefficient is not equal to 1.0,the direction of maximum principal stress is not parallel to the tangent directionof roadway,and the direction of the minimum principal doesn't go through the radial direction of roadway,which causes the change of shear failure direction of surrounding rock.The expansion of plastic zone is controlled by the distribution of maximum shear stress,and the shape of plastic zone deviates from the circle. The peak point curve of shear stress and the boundary of plastic zone change with the change of lateral pressure coefficient,but the boundary of plastic zone always locates at the peak value in the contour of shear stress.The smaller the lateral pressure coefficient,the greater the change of principal stress direction,and the more obvious the irregular shape of plastic zone is.The approximate method for solving the boundary of plastic zone does not consider the effect of plastic zone on the stress in elastic zone,but the shape and development of plastic zone are consistent with the results of numerical simulation.The study has a guiding role in solving engineering problems,which proves that the approximate solution of plastic zone boundary equation is valid.Through the approximate method,the development law of plastic zone in surrounding rock can be obtained.The support technology of butt long bolt can effectively solve the problem of roof fall triggered by the break of cable bolt and the overall subsidence of bolt with overall subsidence of roof,and better eliminate the hidden danger of roof fall.The field test results show that the equation of plastic zone has a theoretical significance and engineering application value.
At present,it is difficult to obtain the exact analytical solution of elastic-plastic problem of circular roadway under bidirectional non-axisymmetric stress. Based on Mohr-Coulomb strength criterion,the approximate boundary equation of plastic zone is studied by substituting Kirsch equation into plastic condition. Also,the influencing factors and mechanics mechanism of formation of plastic zone are analyzed. The results show that the lateral pressure coefficient affects the shape of plastic zone,the direction of in-situ stresses affects the position of butterfly leaf of butterflyshaped plastic zone,and the radius and lithology of roadway affect the radius of plastic zone.When the value of lateral pressure coefficient is not equal to 1.0,the direction of maximum principal stress is not parallel to the tangent directionof roadway,and the direction of the minimum principal doesn't go through the radial direction of roadway,which causes the change of shear failure direction of surrounding rock.The expansion of plastic zone is controlled by the distribution of maximum shear stress,and the shape of plastic zone deviates from the circle. The peak point curve of shear stress and the boundary of plastic zone change with the change of lateral pressure coefficient,but the boundary of plastic zone always locates at the peak value in the contour of shear stress.The smaller the lateral pressure coefficient,the greater the change of principal stress direction,and the more obvious the irregular shape of plastic zone is.The approximate method for solving the boundary of plastic zone does not consider the effect of plastic zone on the stress in elastic zone,but the shape and development of plastic zone are consistent with the results of numerical simulation.The study has a guiding role in solving engineering problems,which proves that the approximate solution of plastic zone boundary equation is valid.Through the approximate method,the development law of plastic zone in surrounding rock can be obtained.The support technology of butt long bolt can effectively solve the problem of roof fall triggered by the break of cable bolt and the overall subsidence of bolt with overall subsidence of roof,and better eliminate the hidden danger of roof fall.The field test results show that the equation of plastic zone has a theoretical significance and engineering application value.
引文
[1]马念杰,赵希栋,赵志强,等.深部采动巷道顶板稳定性分析与控制[J].煤炭学报,2015,40(10):2287-2295.MA Nianjie,ZHAO Xidong,ZHAO Zhiqiang,et al. Stability analysis and control technology of mine roadway roof in deep mining[J].Journal of China Coal Society,2015,40(10):2287-2295.
[2]陈立伟,彭建兵,范文,等.基于统一强度理论的非均匀应力场圆形巷道围岩塑性区分析[J].煤炭学报,2007,32(1):20-23.CHEN Liwei,PENG Jianbing,FAN Wen,et al.Analysis of surrounding rock mass plastic zone of round tunnel under nonuniform stress field based on the unified strength theory[J]. Journal of China Coal Society,2007,32(1):20-23.
[3]卡斯特奈.隧道与坑道静力学[M].上海:上海科学技术出版社,1980.
[4]蔡美峰.岩石力学与工程.第2版[M].北京:科学出版社,2013.
[5]萨文,НГ.孔附近的应力集中[M].北京:科学出版社,1960.
[6] DETOURNAY Emmanuel.An approximate statical solution of the elastoplastic interface for the problem of Galin with a cohesive-frictional material[J]. International Journal of Solids&Structures,1986,22(12):1435-1454.
[7]吕爱钟,张晓莉,王少杰.两向不等压圆形隧洞弹塑性解析分析[J].岩石力学与工程学报,2018,37(1):14-22.LAizhong,ZHANG Xiaoli,WANG Shaojie. Analytic method for elasto-plastic analysis of circular tunnels under non-axisymmetric stresses[J]. Chinese Journal of Rock Mechanics and Engineering,2018,37(1):14-22.
[8] TOKAR Gabriel.Generalization of Galin’s problem to frictional materials and discontinuous stress fields[J]. International Journal of Solids&Structures,1990,26(2):129-147.
[9]侯公羽,李晶晶,赵伟伟,等.两向不等压圆形巷道弹塑性摄动解[J].岩石力学与工程学报,2014,33(S2):3639-3647.HOU Gongyu,LI Jingjing,ZHAO Weiwei,et al. Perturbation solutions for elastoplastic problems of circular tunnel under unequal compression[J]. Chinese Journal of Rock Mechanics and Engineering,2014,33(S2):3639-3647.
[10]魏悦广.两向不等压作用下圆形巷道弹塑性分析摄动解[J].岩土工程学报,1990,12(4):11-20.WEI Yueguang. Perturbation solution for elasto-plastic analysis of circular tunnel under unequal compression in two directions[J].Chinese Jounal of Geotechnical Engineering,1990,12(4):11-20.
[11]严克强.不对称荷载作用下圆洞围岩塑性区的估算方法[J].岩土工程学报,1980,2(2):74-79.YAN Keqiang.Estimation method for plastic zone of circular tunnel under unsymmetrical load[J].Chinese Journal of Geotechnical Engineering,1980,2(2):74-79.
[12]赵志强,马念杰,郭晓菲,等.大变形回采巷道蝶叶型冒顶机理与控制[J].煤炭学报,2016,41(12):2932-2939.ZHAO Zhiqiang,MA Nianjie,GUO Xiaofei,et al. Falling principle and support design of butterfly-failure roof in large deformation mining roadways[J]. Journal of China Coal Society,2016,41(12):2932-2939.
[13]马念杰,李季,赵志强.圆形巷道围岩偏应力场及塑性区分布规律研究[J].中国矿业大学学报,2015,44(2):206-213.MA Nianjie,LI Ji,ZHAO Zhiqiang. Distribution of the deviatoric stress field and plastic zone in circular roadway surrounding rock[J]. Journal of China University of Mining&Technology,2015,44(2):206-213.
[14]马念杰,赵希栋,赵志强,等.深部采动巷道顶板稳定性分析与控制[J].煤炭学报,2015,40(10):2287-2295.MA Nianjie,ZHAO Xidong,ZHAO Zhiqiang,et al.Stability analysis and control technology of mine roadway roof in deep mining[J].Journal of China Coal Society,2015,40(10):2287-2295.
[15]王卫军,袁超,余伟健,等.深部高应力巷道围岩预留变形控制技术[J].煤炭学报,2016,41(9):2156-2164.WANG Weijun,YUAN Chao,YU Weijian,et al.Control technology of reserved surrounding rock deformation in deep roadway under high stress[J]. Journal of China Coal Society,2016,41(9):2156-2164.
[16]王卫军,袁超,余伟健,等.深部大变形巷道围岩稳定性控制方法研究[J].煤炭学报,2016,41(12):2921-2931.WANG Weijun,YUAN Chao,YU Weijian,et al. Stability control method of surrounding rock in deep roadway with large deformation[J]. Journal of China Coal Society,2016,41(12):2921-2931.
[17]王卫军,郭罡业,朱永建,等.高应力软岩巷道围岩塑性区恶性扩展过程及其控制[J].煤炭学报,2015,40(12):2747-2754.WANG Weijun,GUO Gangye,ZHU Yongjian,et al. Malignant development process of plastic zone and control technology of high stress and soft rock roadway[J]. Journal of China Coal Society,2015,40(12):2747-2754.
[18]赵志强.大变形回采巷道围岩变形破坏机理与控制方法研究[D].北京:中国矿业大学(北京),2014.ZHAO Zhiqiang. Mechanism of surrounding rock deformation and failure and control method research in large deformation mining roadway[D]. Beijing:China University of Mining&Technology(Beijing),2014.
[19]李宇翔,彭永久,林全坤,等.非对称荷载作用下圆形洞室塑性区边界的近似计算[J].公路工程,2012,37(4):128-131.LI Yuxiang,PENG Yongjiu,LIN Quankun,et al. Approximate calculation for plastic zone boundary of circular cavity under the asymmetric load[J].Highway Engineering,2012,37(4):128-131.
[20] CARRANZA-TORRES C,FAIRHURST C.Application of the Convergence-Confinement method of tunnel design to rock masses that satisfy the Hoek-Brown failure criterion[J].Tunnelling and Underground Space Technology Incorporating Trenchless Technology Research,2000,15(2):187-213.
[21] JAEGER J C,COOK N G W.岩石力学基础[M].北京:科学出版社,1981.
[22]刘金海,孙广京,谭文峰.深埋巷道锚杆破断失效机理[J].湖南科技大学学报(自然科学版),2015,30(2):8-13.LIU Jinhai,SUN Guangjing,TAN Wenfeng. Mechanism of bolt breaking in deep roadway[J]. Journal of Hunan University of Science&Technology(Natural Science Edition),2015,30(2):8-13.
[23]马念杰,赵志强,冯吉成.困难条件下巷道对接长锚杆支护技术[J].煤炭科学技术,2013,41(9):117-121.MA Nianjie,ZHAO Zhiqiang,FENG Jicheng. Technology of butt long bolt or roadway supporting in difficult conditions[J].Coal Science and Technology,2013,41(9):117-121.
[2]陈立伟,彭建兵,范文,等.基于统一强度理论的非均匀应力场圆形巷道围岩塑性区分析[J].煤炭学报,2007,32(1):20-23.CHEN Liwei,PENG Jianbing,FAN Wen,et al.Analysis of surrounding rock mass plastic zone of round tunnel under nonuniform stress field based on the unified strength theory[J]. Journal of China Coal Society,2007,32(1):20-23.
[3]卡斯特奈.隧道与坑道静力学[M].上海:上海科学技术出版社,1980.
[4]蔡美峰.岩石力学与工程.第2版[M].北京:科学出版社,2013.
[5]萨文,НГ.孔附近的应力集中[M].北京:科学出版社,1960.
[6] DETOURNAY Emmanuel.An approximate statical solution of the elastoplastic interface for the problem of Galin with a cohesive-frictional material[J]. International Journal of Solids&Structures,1986,22(12):1435-1454.
[7]吕爱钟,张晓莉,王少杰.两向不等压圆形隧洞弹塑性解析分析[J].岩石力学与工程学报,2018,37(1):14-22.LAizhong,ZHANG Xiaoli,WANG Shaojie. Analytic method for elasto-plastic analysis of circular tunnels under non-axisymmetric stresses[J]. Chinese Journal of Rock Mechanics and Engineering,2018,37(1):14-22.
[8] TOKAR Gabriel.Generalization of Galin’s problem to frictional materials and discontinuous stress fields[J]. International Journal of Solids&Structures,1990,26(2):129-147.
[9]侯公羽,李晶晶,赵伟伟,等.两向不等压圆形巷道弹塑性摄动解[J].岩石力学与工程学报,2014,33(S2):3639-3647.HOU Gongyu,LI Jingjing,ZHAO Weiwei,et al. Perturbation solutions for elastoplastic problems of circular tunnel under unequal compression[J]. Chinese Journal of Rock Mechanics and Engineering,2014,33(S2):3639-3647.
[10]魏悦广.两向不等压作用下圆形巷道弹塑性分析摄动解[J].岩土工程学报,1990,12(4):11-20.WEI Yueguang. Perturbation solution for elasto-plastic analysis of circular tunnel under unequal compression in two directions[J].Chinese Jounal of Geotechnical Engineering,1990,12(4):11-20.
[11]严克强.不对称荷载作用下圆洞围岩塑性区的估算方法[J].岩土工程学报,1980,2(2):74-79.YAN Keqiang.Estimation method for plastic zone of circular tunnel under unsymmetrical load[J].Chinese Journal of Geotechnical Engineering,1980,2(2):74-79.
[12]赵志强,马念杰,郭晓菲,等.大变形回采巷道蝶叶型冒顶机理与控制[J].煤炭学报,2016,41(12):2932-2939.ZHAO Zhiqiang,MA Nianjie,GUO Xiaofei,et al. Falling principle and support design of butterfly-failure roof in large deformation mining roadways[J]. Journal of China Coal Society,2016,41(12):2932-2939.
[13]马念杰,李季,赵志强.圆形巷道围岩偏应力场及塑性区分布规律研究[J].中国矿业大学学报,2015,44(2):206-213.MA Nianjie,LI Ji,ZHAO Zhiqiang. Distribution of the deviatoric stress field and plastic zone in circular roadway surrounding rock[J]. Journal of China University of Mining&Technology,2015,44(2):206-213.
[14]马念杰,赵希栋,赵志强,等.深部采动巷道顶板稳定性分析与控制[J].煤炭学报,2015,40(10):2287-2295.MA Nianjie,ZHAO Xidong,ZHAO Zhiqiang,et al.Stability analysis and control technology of mine roadway roof in deep mining[J].Journal of China Coal Society,2015,40(10):2287-2295.
[15]王卫军,袁超,余伟健,等.深部高应力巷道围岩预留变形控制技术[J].煤炭学报,2016,41(9):2156-2164.WANG Weijun,YUAN Chao,YU Weijian,et al.Control technology of reserved surrounding rock deformation in deep roadway under high stress[J]. Journal of China Coal Society,2016,41(9):2156-2164.
[16]王卫军,袁超,余伟健,等.深部大变形巷道围岩稳定性控制方法研究[J].煤炭学报,2016,41(12):2921-2931.WANG Weijun,YUAN Chao,YU Weijian,et al. Stability control method of surrounding rock in deep roadway with large deformation[J]. Journal of China Coal Society,2016,41(12):2921-2931.
[17]王卫军,郭罡业,朱永建,等.高应力软岩巷道围岩塑性区恶性扩展过程及其控制[J].煤炭学报,2015,40(12):2747-2754.WANG Weijun,GUO Gangye,ZHU Yongjian,et al. Malignant development process of plastic zone and control technology of high stress and soft rock roadway[J]. Journal of China Coal Society,2015,40(12):2747-2754.
[18]赵志强.大变形回采巷道围岩变形破坏机理与控制方法研究[D].北京:中国矿业大学(北京),2014.ZHAO Zhiqiang. Mechanism of surrounding rock deformation and failure and control method research in large deformation mining roadway[D]. Beijing:China University of Mining&Technology(Beijing),2014.
[19]李宇翔,彭永久,林全坤,等.非对称荷载作用下圆形洞室塑性区边界的近似计算[J].公路工程,2012,37(4):128-131.LI Yuxiang,PENG Yongjiu,LIN Quankun,et al. Approximate calculation for plastic zone boundary of circular cavity under the asymmetric load[J].Highway Engineering,2012,37(4):128-131.
[20] CARRANZA-TORRES C,FAIRHURST C.Application of the Convergence-Confinement method of tunnel design to rock masses that satisfy the Hoek-Brown failure criterion[J].Tunnelling and Underground Space Technology Incorporating Trenchless Technology Research,2000,15(2):187-213.
[21] JAEGER J C,COOK N G W.岩石力学基础[M].北京:科学出版社,1981.
[22]刘金海,孙广京,谭文峰.深埋巷道锚杆破断失效机理[J].湖南科技大学学报(自然科学版),2015,30(2):8-13.LIU Jinhai,SUN Guangjing,TAN Wenfeng. Mechanism of bolt breaking in deep roadway[J]. Journal of Hunan University of Science&Technology(Natural Science Edition),2015,30(2):8-13.
[23]马念杰,赵志强,冯吉成.困难条件下巷道对接长锚杆支护技术[J].煤炭科学技术,2013,41(9):117-121.MA Nianjie,ZHAO Zhiqiang,FENG Jicheng. Technology of butt long bolt or roadway supporting in difficult conditions[J].Coal Science and Technology,2013,41(9):117-121.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |