深部洞室开挖卸荷分区破裂机制的动力分析
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摘要
随着地下工程开挖深度的增加,深部岩体将处于高应力和复杂的地质环境中,产生与浅埋洞室破坏模式迥异的分区破裂现象。深部洞室在动力卸荷作用下,基于应变梯度理论和损伤软化模型,建立了弹塑性损伤软化动力模型,推导了含有应变梯度项的运动方程、平衡方程和边界条件,提出相应的破坏判据,采用Runge-Kutta方法和Matlab数值软件求得不同卸载时刻围岩附加位移场、应力场和开挖后围岩总位移场、应力场,得到深部洞室围岩分区破裂的动态形成过程和发展规律。由理论计算值与地质力学模型试验实测值对比分析得知,围岩的径向位移、径向应力和切向应力出现波峰和波谷交替振荡的变化规律,理论计算得到的破裂区和非破裂区的宽度和数量与试验实测值有很好的一致性,证实了该模型分析分区破裂现象的适用性,对以后深部地下工程围岩变形破坏和支护设计提供理论支持。
With the increase of excavation depth, the deep rock mass is in high stress and complicated geological environment and the zonal disintegration phenomenon is observed at some projects, which is largely different from failure modes of shallow caverns. Under the action of dynamic unloading, an elastoplastic damage softening dynamic model is put forward based on the strain gradient theory and damage softening model. The dynamical equation, the equilibrium equations, boundary conditions and the failure criterion are deduced by considering the strain gradient. The theoretical solutions of radial displacement, radial stresses and tangential stresses of deep surrounding rock mass at different unloading times are calculated by Runge-Kutta and Matlab. The total displacement and stress fields of surrounding rock are also obtained after excavation. The dynamic formation and development regularity of zonal disintegration in deep caverns are achieved. The radial displacement, radial stresses and tangential stresses of deep surrounding rock mass are exhibited as an oscillating mode. The number and the width of zonal disintegration are in good agreement with the data of model tests. The applicability of the elastoplastic damage softening dynamic model for zonal disintegration in the explanation of zonal disintegration is confirmed. This model can also be used to provide theoretical support for the deformation and failure of surrounding rock in deep underground engineering.
With the increase of excavation depth, the deep rock mass is in high stress and complicated geological environment and the zonal disintegration phenomenon is observed at some projects, which is largely different from failure modes of shallow caverns. Under the action of dynamic unloading, an elastoplastic damage softening dynamic model is put forward based on the strain gradient theory and damage softening model. The dynamical equation, the equilibrium equations, boundary conditions and the failure criterion are deduced by considering the strain gradient. The theoretical solutions of radial displacement, radial stresses and tangential stresses of deep surrounding rock mass at different unloading times are calculated by Runge-Kutta and Matlab. The total displacement and stress fields of surrounding rock are also obtained after excavation. The dynamic formation and development regularity of zonal disintegration in deep caverns are achieved. The radial displacement, radial stresses and tangential stresses of deep surrounding rock mass are exhibited as an oscillating mode. The number and the width of zonal disintegration are in good agreement with the data of model tests. The applicability of the elastoplastic damage softening dynamic model for zonal disintegration in the explanation of zonal disintegration is confirmed. This model can also be used to provide theoretical support for the deformation and failure of surrounding rock in deep underground engineering.
引文
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[7]李树忱,钱七虎,张敦福,等.深埋隧道开挖过程动态及破裂形态分析[J].岩石力学与工程学报,2009,28(10):2104-2112.LI Shu-chen,QIAN Qi-hu,ZHANG Dun-fu,et al.Analysis of dynamic and fractured phenomena for excavation process of deep tunnel[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(10):2104-2112.
[8]周小平,钱七虎.深埋巷道分区破裂化机制[J].岩石力学与工程学报,2007,26(5):877-885.ZHOU Xiao-ping,QIAN Qi-hu.Zonal fracturing mechanism in deep tunnel[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(5):877-885.
[9]陈胜宏,王鸿儒,熊文林.节理岩体的偶应力影响研究[J].水利学报,1990,1(1):44-48.CHEN Sheng-hong,WANG Hong-ru,XIONG Wen-lin.The effect of couple stress on jointed rock mass[J].Journal of Hydraulic Engineering,1990,1(1):44-48.
[10]王学滨,张智慧,潘一山.基于梯度塑性理论的岩样拉压剪破坏统一失稳判据[J].岩土力学,2003,24(增刊):138-142.WANG Xue-bin,ZHANG Zhi-hui,PAN Yi-shan.Unified formula for instability criterion under uniaxial tension direct shear and uniaxial compression subjected to shear failure based on gradient-dependent plasticity[J].Rock and Soil Mechanics,2003,24(Supp.):138-142.
[11]王学滨,潘一山,任伟杰.基于应变梯度理论的岩石试件剪切破坏失稳判据[J].岩石力学与工程学报,2003,22(5):747-750.WANG Xue-bin,PAN Yi-shan,REN Wei-jie.Instability of shear failure for rock specimen based on gradient oriented plasticity[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(5):747-750.
[12]张绪涛,张强勇,向文,等.基于应变梯度理论的分区破裂机制分析研究[J].岩石力学与工程学报,2016,35(4):724-734.ZHANG Xu-tao,ZHANG Qiang-yong,XIANG Wen,et al.Zonal disintegration mechanism based on strain gradient theory[J].Chinese Journal of Rock Mechanics and Engineering,2014,35(4):724-734.
[13]MINDLIN R D.Micro-structure in linear elasticity[J].Archive for Rational Mechanics and Analysis,1964,16(1):51-78.
[14]MINDLIN R D.Second gradient of strain and surface tension in linear elasticity[J].International Journal of Solids and Structures,1965,1(4):417-438.
[15]ESHEL N N,ROSENFELD G.Axisymmetric problems in elastic materials of grade two[J].Journal of the Franklin Institute,1975,299(1):43-51.
[16]YANG F,CHONG A C M,LAM D C C.Couple stress based strain gradient theory for elasticity[J].International Journal of Solids and Structures,2002,39(10):2731-2743.
[17]LAM D C C,YANG F,CHONG A C M.Experiments and theory in strain gradient elasticity[J].Journal of the Mechanics and Physics of Solids,2003,51(8):1477-1508.
[18]何满潮,谢和平,彭苏萍,等.深部开采岩体力学研究[J].岩石力学与工程学报,2005,24(16):2803-2813.HE Man-chao,XIE He-ping,PENG Su-ping,et al.Study on rock mechanics in deep mining engineering[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(16):2803-2813.
[19]刘冬桥,王焯,张晓云.岩石应变软化变形特性及损伤本构模型研究[J].岩土力学,2017,38(10):2901-2908.LIU Dong-qiao,WANG Zhuo,ZHANG Xiao-yun.Characteristics of strain softening of rocks and its damage constitutive model[J].Rock and Soil Mechanics,2017,38(10):2901-2908.
[20]戚承志,钱七虎.岩体动力变形与破坏的基本问题[M].北京:科学出版社,2009.QI Cheng-zhi,QIAN Qi-hu.Basic problems for the dynamic deformation and fracture of rock[M].Beijing:Science Press,2009:63-70.
[21]张俊文.深部大规模松软围岩巷道破坏分区理论分析[J].中国矿业大学学报,2017,46(2):292-299.ZHANG Jun-wen.Theoretical analysis on failure zone of surrounding rock in deep large-scale soft rock roadway[J].Journal of China University of Mining and Technology,2017,46(2):292-299.
[22]张绪涛.深部洞室分区破裂机制与数值模拟分析研究[D].济南:山东大学,2015.ZHANG Xu-tao.The research on failure mechanism and numerical simulation and analysis of zonal disintegration in deep tunnel[D].Jinan:Shandong University,2015.
[23]王学滨.岩样单轴压缩峰后泊松比理论研究[J].工程力学,2006,23(4):99-103.WANG Xue-bin.Analysis of the post-peak Poisson’s ratio of rock specimens in uniaxial compression[J].Engineering Mechanics,2006,23(4):99-103.
[24]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.ZHANG Chang-guang,FAN Wen,ZHAO Jun-hai.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.
[25]ZHAO JIDONG,PEDROSO DORIVAL.Strain gradient theory in orthogonal curvilinear coordinates[J].International Journal of Solids and Structures,2008,45(11-12):3507-3520.
[26]周小平,毕靖,钱七虎.动态开挖卸荷条件下深埋圆形洞室各向同性围岩的分区破裂化机制[J].固体力学学报,2013,34(4):352-360.ZHOU Xiao-ping,BI Jing,QIAN Qi-hu.Zonal disintegration mechanism of isotropic surrounding rock in deep buried circular tunnel under dynamic excavation unloading[J].Chinese Journal of Solid Mechanics,2013,34(4):352-360.
[27]袁璞.爆炸荷载作用下深部岩体分区破裂模型试验研究[D].合肥:安徽理工大学,2016.YUAN Pu.Experimental study on zonal disintegration in deep rock mass under blasting load[D].Hefei:Anhui University of Science and Technology,2016.
[28]章晓.求解波动方程的近似解析指数时间差分方法及其数值模拟[D].北京:清华大学,2013.ZHANG Xiao.A nearly analytic exponential time difference method for solving wave equations and its numerical simulation[D].Beijing:Tsinghua University,2013.
[29]陈山.求解波动方程的龙格-库塔型方法及其地震波传播模拟[D].北京:清华大学,2010.CHEN Shan.The Runge-Kutta type method for solving wave equations and its simulation of seismic wave propagation[D].Beijing:Tsinghua University,2010.
[30]李凯锐.深部围岩分区破裂梯度模型的数值研究[D].北京:北京建筑大学,2014.LI Rui-kai.The numerical study of the strain gradient model of zonal disintegration of rock mass near deep level tunnels[D].Beijing:Beijing University of Civil Engineering and Architecture,2014.
[31]戚承志,钱七虎.岩体动力变形破坏的基本问题[M]北京:科学出版社,2009:322-342.QI Cheng-zhi,QIAN Qi-hu.Basic problems of dynamic deformation and fracture of rock mass[M].Beijing:Science Press,2009:322-342.
[32]张强勇,张绪涛,向文,等.不同洞形与加载方式对深部岩体分区破裂影响的模型试验研究[J].岩石力学与工程学报,2013,32(8):1564-1571.ZHANG Qiang-yong,ZHANG Xu-tao,XIANG Wen,et al.Model test study of zonal disintegration in deep rock mass under different cavern shapes and loading conditions[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(8):1564-1571.
[33]张绪涛,张强勇,向文,等.深部层状节理岩体分区破裂模型试验研究[J].岩土力学,2014,35(8):2247-2254.ZHANG Xu-tao,ZHANG Qiang-yong,XIANG Wen,et al.Model test study of zonal disintegration in deep layered jointed rock mass[J].Rock and Soil Mechanics,2014,35(8):2247-2254.
[2]钱七虎.深部地下工空间开发中的关键科学问题[C]//深部地下空间开发中的基础研究关键技术问题.北京:科学出版社,2004.QIAN Qi-hu.The key problems of deep underground space development[C]//Key Technical Problems of Base Research in Deep Underground Space Development.Beijing:Science Press,2004.
[3]SHEMYAKIN E I,FISENKO G L,KURLENYA M V,et al.Zonal disintegration of rocks around underground workings,part I:data of in-situ observations[J].Soviet Mining,1986,22(3):157-168.
[4]李术才,王汉鹏,钱七虎,等.深部巷道围岩分区破裂化现象现场监测研究[J].岩石力学与工程学报,2008,27(8):1545-1553.LI Shu-cai,WANG Han-peng,QIAN Qi-hu,et al.In-situ monitoring research on zonal disintegration of surrounding rock mass in deep mine roadways[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(8):1545-1553.
[5]顾金才,顾雷雨,陈安敏,等.深部开挖洞室围岩分层断裂破坏机制模型试验研究[J].岩石力学与工程学报,2008,27(3):433-438.GU Jin-cai,GU Lei-yu,CHEN An-min,et al.Model test study on mechanism of layered fracture within surrounding rock of tunnels in deep stratum[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(3):433-438.
[6]张强勇,陈旭光,林波,等.深部巷道围岩分区破裂三维地质力学模型试验研究[J].岩石力学与工程学报,2009,28(9):1757-1766.ZHANG Qiang-yong,CHEN Xu-guang,LIN Bo,et al.Study of 3D geomechanical model test of zonal disintegration of surrounding rock of deep tunnel[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(9):1757-1766.
[7]李树忱,钱七虎,张敦福,等.深埋隧道开挖过程动态及破裂形态分析[J].岩石力学与工程学报,2009,28(10):2104-2112.LI Shu-chen,QIAN Qi-hu,ZHANG Dun-fu,et al.Analysis of dynamic and fractured phenomena for excavation process of deep tunnel[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(10):2104-2112.
[8]周小平,钱七虎.深埋巷道分区破裂化机制[J].岩石力学与工程学报,2007,26(5):877-885.ZHOU Xiao-ping,QIAN Qi-hu.Zonal fracturing mechanism in deep tunnel[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(5):877-885.
[9]陈胜宏,王鸿儒,熊文林.节理岩体的偶应力影响研究[J].水利学报,1990,1(1):44-48.CHEN Sheng-hong,WANG Hong-ru,XIONG Wen-lin.The effect of couple stress on jointed rock mass[J].Journal of Hydraulic Engineering,1990,1(1):44-48.
[10]王学滨,张智慧,潘一山.基于梯度塑性理论的岩样拉压剪破坏统一失稳判据[J].岩土力学,2003,24(增刊):138-142.WANG Xue-bin,ZHANG Zhi-hui,PAN Yi-shan.Unified formula for instability criterion under uniaxial tension direct shear and uniaxial compression subjected to shear failure based on gradient-dependent plasticity[J].Rock and Soil Mechanics,2003,24(Supp.):138-142.
[11]王学滨,潘一山,任伟杰.基于应变梯度理论的岩石试件剪切破坏失稳判据[J].岩石力学与工程学报,2003,22(5):747-750.WANG Xue-bin,PAN Yi-shan,REN Wei-jie.Instability of shear failure for rock specimen based on gradient oriented plasticity[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(5):747-750.
[12]张绪涛,张强勇,向文,等.基于应变梯度理论的分区破裂机制分析研究[J].岩石力学与工程学报,2016,35(4):724-734.ZHANG Xu-tao,ZHANG Qiang-yong,XIANG Wen,et al.Zonal disintegration mechanism based on strain gradient theory[J].Chinese Journal of Rock Mechanics and Engineering,2014,35(4):724-734.
[13]MINDLIN R D.Micro-structure in linear elasticity[J].Archive for Rational Mechanics and Analysis,1964,16(1):51-78.
[14]MINDLIN R D.Second gradient of strain and surface tension in linear elasticity[J].International Journal of Solids and Structures,1965,1(4):417-438.
[15]ESHEL N N,ROSENFELD G.Axisymmetric problems in elastic materials of grade two[J].Journal of the Franklin Institute,1975,299(1):43-51.
[16]YANG F,CHONG A C M,LAM D C C.Couple stress based strain gradient theory for elasticity[J].International Journal of Solids and Structures,2002,39(10):2731-2743.
[17]LAM D C C,YANG F,CHONG A C M.Experiments and theory in strain gradient elasticity[J].Journal of the Mechanics and Physics of Solids,2003,51(8):1477-1508.
[18]何满潮,谢和平,彭苏萍,等.深部开采岩体力学研究[J].岩石力学与工程学报,2005,24(16):2803-2813.HE Man-chao,XIE He-ping,PENG Su-ping,et al.Study on rock mechanics in deep mining engineering[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(16):2803-2813.
[19]刘冬桥,王焯,张晓云.岩石应变软化变形特性及损伤本构模型研究[J].岩土力学,2017,38(10):2901-2908.LIU Dong-qiao,WANG Zhuo,ZHANG Xiao-yun.Characteristics of strain softening of rocks and its damage constitutive model[J].Rock and Soil Mechanics,2017,38(10):2901-2908.
[20]戚承志,钱七虎.岩体动力变形与破坏的基本问题[M].北京:科学出版社,2009.QI Cheng-zhi,QIAN Qi-hu.Basic problems for the dynamic deformation and fracture of rock[M].Beijing:Science Press,2009:63-70.
[21]张俊文.深部大规模松软围岩巷道破坏分区理论分析[J].中国矿业大学学报,2017,46(2):292-299.ZHANG Jun-wen.Theoretical analysis on failure zone of surrounding rock in deep large-scale soft rock roadway[J].Journal of China University of Mining and Technology,2017,46(2):292-299.
[22]张绪涛.深部洞室分区破裂机制与数值模拟分析研究[D].济南:山东大学,2015.ZHANG Xu-tao.The research on failure mechanism and numerical simulation and analysis of zonal disintegration in deep tunnel[D].Jinan:Shandong University,2015.
[23]王学滨.岩样单轴压缩峰后泊松比理论研究[J].工程力学,2006,23(4):99-103.WANG Xue-bin.Analysis of the post-peak Poisson’s ratio of rock specimens in uniaxial compression[J].Engineering Mechanics,2006,23(4):99-103.
[24]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.ZHANG Chang-guang,FAN Wen,ZHAO Jun-hai.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.
[25]ZHAO JIDONG,PEDROSO DORIVAL.Strain gradient theory in orthogonal curvilinear coordinates[J].International Journal of Solids and Structures,2008,45(11-12):3507-3520.
[26]周小平,毕靖,钱七虎.动态开挖卸荷条件下深埋圆形洞室各向同性围岩的分区破裂化机制[J].固体力学学报,2013,34(4):352-360.ZHOU Xiao-ping,BI Jing,QIAN Qi-hu.Zonal disintegration mechanism of isotropic surrounding rock in deep buried circular tunnel under dynamic excavation unloading[J].Chinese Journal of Solid Mechanics,2013,34(4):352-360.
[27]袁璞.爆炸荷载作用下深部岩体分区破裂模型试验研究[D].合肥:安徽理工大学,2016.YUAN Pu.Experimental study on zonal disintegration in deep rock mass under blasting load[D].Hefei:Anhui University of Science and Technology,2016.
[28]章晓.求解波动方程的近似解析指数时间差分方法及其数值模拟[D].北京:清华大学,2013.ZHANG Xiao.A nearly analytic exponential time difference method for solving wave equations and its numerical simulation[D].Beijing:Tsinghua University,2013.
[29]陈山.求解波动方程的龙格-库塔型方法及其地震波传播模拟[D].北京:清华大学,2010.CHEN Shan.The Runge-Kutta type method for solving wave equations and its simulation of seismic wave propagation[D].Beijing:Tsinghua University,2010.
[30]李凯锐.深部围岩分区破裂梯度模型的数值研究[D].北京:北京建筑大学,2014.LI Rui-kai.The numerical study of the strain gradient model of zonal disintegration of rock mass near deep level tunnels[D].Beijing:Beijing University of Civil Engineering and Architecture,2014.
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