隧道围岩结构地震动稳定性分析的动力有限元强度折减法
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摘要
为了得到隧道围岩结构的地震动安全系数,借助通用有限元软件ANSYS,首先对水平地震作用下的模型进行模态分析,得到质量阻尼系数和刚度阻尼系数;其次由静力分析模型得到竖向边界上的水平向支座反力,然后将结构自重转化为温度边界条件,通过热分析得到模型各节点的温度,从而实现在动力分析中考虑重力的影响;最后采用悬臂梁动力分析模型,导入热分析获得的模型各节点的温度,并在竖向边界上施加水平向支座反力,通过不断折减围岩塑性区的凝聚力c和内摩擦角Φ,直到计算不收敛为止,从而得到隧道围岩结构的地震动安全系数。数值算例结果表明:采用的方法是可行的,将围岩结构自重转化为节点温度的措施解决了以往动力分析不能考虑结构自重的难点,进而为以后地震作用下隧道动力安全系数的计算及其工程应用提供了理论依据。
In order to obtain earthquake safety factor of surrounding rock of tunnel,using FEM software ANSYS,firstly,modal analysis is done by adopting the model under the horizontal earthquake action;and then mass damping coefficient and stiffness damping coefficient are obtained.Secondly,the horizontal support reaction force along the vertical borders is obtained by the static analysis.Thirdly,for considering the gravity influence in dynamic analysis,structure gravity is become into temperature boundary condition;and the temperature of each node in model is obtained by thermal analysis.Finally,adopting the dynamic analysis model of cantilever beam,and inputting into the node temperature which is obtained by using thermal analysis,and applying the level support reaction force along the vertical borders,cohesion c and friction angle? in plastic zone are continuously discounted until the calculation is not convergent;and then the earthquake safety factor of surrounding rock of tunnel is obtained.Numerical example result shows that this approach is feasible,the measure that the structure gravity is become into the node temperature solves the difficulty that the structure gravity can not be considered in previous dynamic analysis;and so a theoretical basis is provided for dynamic safety factor calculation and engineering application of surrounding rock of tunnel under earthquake.
In order to obtain earthquake safety factor of surrounding rock of tunnel,using FEM software ANSYS,firstly,modal analysis is done by adopting the model under the horizontal earthquake action;and then mass damping coefficient and stiffness damping coefficient are obtained.Secondly,the horizontal support reaction force along the vertical borders is obtained by the static analysis.Thirdly,for considering the gravity influence in dynamic analysis,structure gravity is become into temperature boundary condition;and the temperature of each node in model is obtained by thermal analysis.Finally,adopting the dynamic analysis model of cantilever beam,and inputting into the node temperature which is obtained by using thermal analysis,and applying the level support reaction force along the vertical borders,cohesion c and friction angle? in plastic zone are continuously discounted until the calculation is not convergent;and then the earthquake safety factor of surrounding rock of tunnel is obtained.Numerical example result shows that this approach is feasible,the measure that the structure gravity is become into the node temperature solves the difficulty that the structure gravity can not be considered in previous dynamic analysis;and so a theoretical basis is provided for dynamic safety factor calculation and engineering application of surrounding rock of tunnel under earthquake.
引文
[1]史良.黄土隧道抗震设计研究[D].西安:长安大学,2005.
[2]KOLYMBAS D.Tunnelling and tunnel mechanics:A rational approach to tunnelling[M].Berlin,Heidelberg:Springer,2005.
[3]陈国兴.岩土地震工程学[M].北京:科学出版社,2007.
[4]陈国兴,张克绪,谢君斐.黄土崖窑洞抗震性能分析[J].哈尔滨建筑大学学报,1995,28(1):16-21.CHEN Guo-xing,ZHANG Ke-xu,XIE Jun-fei.Aseismic performance analysis of the cave dewlling on the loess precipice[J].Journal of Harbin University of Civil Engineering and Architecture,1995,28(1):16-21.
[5]高峰,任侠.黄土窑洞地震反应分析[J].兰州铁道学院学报(自然科学版),2001,20(3):12-18.GAO Feng,REN Xia.Seimic responses analysis of a loess cave[J].Journal of Lanzhou Railway University(Natural Sciences),2001,20(3):12-18.
[6]邱陈瑜,郑颖人,宋雅坤.采用ANSYS软件讨论无衬砌黄土隧洞安全系数[J].地下空间与工程学报,2009,5(2):291-296.QIU Chen-yu,ZHENG Ying-ren,SONG Ya-kun.Exploring the safety factors of unlined loess tunnel by ANSYS[J].Chinese Journal of Underground Space and Engineering,2009,5(2):291-296.
[7]郑颖人,邱陈瑜,张红,等.关于土体隧洞围岩稳定性分析方法的探索[J].岩石力学与工程学报,2008,27(10):254-260.ZHENG Ying-ren,QIU Chen-yu,ZHANG Hong,et al.Exploration of stability analysis methods of surrounding rocks in soil tunnel[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(10):254-260.
[8]张红,郑颖人,杨臻,等.黄土隧洞安全系数初探[J].地下空间与工程学报,2009,5(2):291-296.ZHANG Hong,ZHENG Ying-ren,YANG Zhen,et al.Exploration of safety factors of the loess tunnel[J].Chinese Journal of Underground Space and Engineering,2009,5(2):297-306.
[9]杨臻,郑颖人,张红,等.岩质隧洞围岩稳定性分析与强度参数的探讨[J].地下空间与工程学报,2009,5(2):283-290.YANG Zhen,ZHENG Ying-ren,ZHANG Hong,et al.Analysis of stability for the surrounding rock of tunnel and exploring the strength parameters[J].Chinese Journal of Underground Space and Engineering,2009,5(2):283-290.
[10]张黎明,郑颖人,王在泉,等.有限元强度折减法在公路隧道中的应用探讨[J].岩土力学,2007,28(1):97-101.ZHANG Li-ming,ZHENG Ying-ren,WANG Zai-quan,et al.Application of strength reduction finite element method to road tunnels[J].Rock and Soil Mechanics,2007,28(1):97-101.
[11]江权,冯夏庭,向天兵.基于强度折减原理的地下洞室群整体安全系数计算方法探讨[J].岩土力学,2009,30(8):2483-2488.JIANG Quan,FENG Xia-ting,XIANG Tian-bing.Discussion on method for calculating general safety factor of underground caverns based on strength reduction theory[J].Rock and Soil Mechanics,2009,30(8):2483-2488.
[12]李树忱,李术才,徐帮树.隧道围岩稳定分析的最小安全系数法[J].岩土力学,2007,28(3):549-554.LI Shu-chen,LI Shu-cai,XU Bang-shu.Minimum safety factor method for stability analysis of surrounding rockmass of tunnel[J].Rock and Soil Mechanics,2007,28(3):549-554.
[13]YANG X L,HUANG F.Stability analysis of shallow tunnels subjected to seepage with strength reduction theory[J].Journal of Central South University of Technology,2009,16(6):1001-1005.
[14]STERPIL D,CIVIDINI A.A physical and numerical investigation on the stability of shallow tunnels in strain softening media[J].Rock Mechanics and Rock Engineering,2004,37(4):277-298.
[15]ZARETSKIIL Y K,KARABAEVL M I,KHACHATURYAN N S.Construction monitoring of a shallow tunnel in the Lefortovo District of Moscow[J].Soil Mechanics and Foundation Engineering,2004,41(2):45-51.
[16]许增会,刘刚.地震区隧道稳定性分析方法[J].公路,2004,(10):189-193.XU Zeng-hui,LIU Gang.A study of stability analysis of tunnels in seismic region[J].Highway,2004,(10):189-193.
[17]刘晶波,李彬,刘祥庆.地下结构抗震设计中的静力弹塑性分析方法[J].土木工程学报,2007,47(7):68-76.LIU Jing-bo,LI Bin,LIU Xiang-qing.A static elasto-plastic analysis method in seismic design of underground structures[J].China Civil Engineering Journal,2007,47(7):68-76.
[18]程选生,郑颖人.地震作用下无衬砌黄土隧道围岩结构安全系数的计算探讨[J].岩土力学,2011,32(3):769-774.CHENG Xuan-sheng,ZHENG Ying-ren.Calculation discussion about safety factor of unlined loess tunnel wall rock structure under earthquake[J].Rock and Soil Mechanics,2011,32(3):769-774.
[19]谷兆祺,彭守拙,李仲奎.地下洞室工程[M].北京:清华大学出版社,1994.
[20]CHENG X S,TIAN R R,WANG J L.Parameter determination about loess tunnel analysis model under earthquake action[C]//Proceedings of the Eleventh International Symposium on Structural Engineering.Guangzhou City:Science Press,2010:34-38.
[21]陈立伟,彭建兵,范文,等.地震作用下黄土暗穴的稳定性[J].长安大学学报(自然科学版),2007,27(6):34-36.CHEN Li-wei,PENG Jian-bing,FAN Wen,et al.Stability of loess hidden hole under earthquake[J].Journal of Chang’an University(Natural Science Edition),2007,27(6):34-36.
[22]彭建兵,李庆春,陈志新,等.黄土洞穴灾害[M].北京:科学出版社,2008.
[23]王勖成,邵敏.有限单元法基本原理和数值方法[M].北京:清华大学出版社(第二版),2000.
[24]郑颖人,陈祖煜,王恭先,等.边坡与滑坡工程治理[M].北京:人民交通出版社,2007.
[25]郑颖人,赵尚毅,邓楚键,等.有限元极限分析法发展及其在岩土工程中的应用[J].中国工程科学,2006,8(12):39-61.ZHENG Ying-ren,ZHAO Shang-yi,DENG Chu-jian,et al.Development of finite element limit analysis method and its applications in geotechnical engineering[J].Engineering Sciences,2006,8(12):39-61.
[26]郑颖人,赵尚毅,张鲁渝.用有限元强度折减法进行边坡稳定分析[J].中国工程科学,2002,4(10):57-62.ZHNG Ying-ren,ZHAO Shang-yi,ZHANG Lu-yu.Slope stability analysis by strength reduction FEM[J].Engineering Science,2002,4(10):57-62.
[27]王峻,王兰民,李兰.永登5.8级地震中黄土震陷灾害的探讨[J].地震研究,2005,28(4):393-397.WANG Jun,WANG Lan-min,LI Lan.Discussion on the loess subsidence disaster caused by the Yongdeng M5.8 earthquake[J].Journal of Seimological Research,2005,28(4):393-397.
[28]中华人民共和国建设部.GB 50011-2001建筑抗震设计规范[S].北京:中国建筑工业出版社,2001.
[2]KOLYMBAS D.Tunnelling and tunnel mechanics:A rational approach to tunnelling[M].Berlin,Heidelberg:Springer,2005.
[3]陈国兴.岩土地震工程学[M].北京:科学出版社,2007.
[4]陈国兴,张克绪,谢君斐.黄土崖窑洞抗震性能分析[J].哈尔滨建筑大学学报,1995,28(1):16-21.CHEN Guo-xing,ZHANG Ke-xu,XIE Jun-fei.Aseismic performance analysis of the cave dewlling on the loess precipice[J].Journal of Harbin University of Civil Engineering and Architecture,1995,28(1):16-21.
[5]高峰,任侠.黄土窑洞地震反应分析[J].兰州铁道学院学报(自然科学版),2001,20(3):12-18.GAO Feng,REN Xia.Seimic responses analysis of a loess cave[J].Journal of Lanzhou Railway University(Natural Sciences),2001,20(3):12-18.
[6]邱陈瑜,郑颖人,宋雅坤.采用ANSYS软件讨论无衬砌黄土隧洞安全系数[J].地下空间与工程学报,2009,5(2):291-296.QIU Chen-yu,ZHENG Ying-ren,SONG Ya-kun.Exploring the safety factors of unlined loess tunnel by ANSYS[J].Chinese Journal of Underground Space and Engineering,2009,5(2):291-296.
[7]郑颖人,邱陈瑜,张红,等.关于土体隧洞围岩稳定性分析方法的探索[J].岩石力学与工程学报,2008,27(10):254-260.ZHENG Ying-ren,QIU Chen-yu,ZHANG Hong,et al.Exploration of stability analysis methods of surrounding rocks in soil tunnel[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(10):254-260.
[8]张红,郑颖人,杨臻,等.黄土隧洞安全系数初探[J].地下空间与工程学报,2009,5(2):291-296.ZHANG Hong,ZHENG Ying-ren,YANG Zhen,et al.Exploration of safety factors of the loess tunnel[J].Chinese Journal of Underground Space and Engineering,2009,5(2):297-306.
[9]杨臻,郑颖人,张红,等.岩质隧洞围岩稳定性分析与强度参数的探讨[J].地下空间与工程学报,2009,5(2):283-290.YANG Zhen,ZHENG Ying-ren,ZHANG Hong,et al.Analysis of stability for the surrounding rock of tunnel and exploring the strength parameters[J].Chinese Journal of Underground Space and Engineering,2009,5(2):283-290.
[10]张黎明,郑颖人,王在泉,等.有限元强度折减法在公路隧道中的应用探讨[J].岩土力学,2007,28(1):97-101.ZHANG Li-ming,ZHENG Ying-ren,WANG Zai-quan,et al.Application of strength reduction finite element method to road tunnels[J].Rock and Soil Mechanics,2007,28(1):97-101.
[11]江权,冯夏庭,向天兵.基于强度折减原理的地下洞室群整体安全系数计算方法探讨[J].岩土力学,2009,30(8):2483-2488.JIANG Quan,FENG Xia-ting,XIANG Tian-bing.Discussion on method for calculating general safety factor of underground caverns based on strength reduction theory[J].Rock and Soil Mechanics,2009,30(8):2483-2488.
[12]李树忱,李术才,徐帮树.隧道围岩稳定分析的最小安全系数法[J].岩土力学,2007,28(3):549-554.LI Shu-chen,LI Shu-cai,XU Bang-shu.Minimum safety factor method for stability analysis of surrounding rockmass of tunnel[J].Rock and Soil Mechanics,2007,28(3):549-554.
[13]YANG X L,HUANG F.Stability analysis of shallow tunnels subjected to seepage with strength reduction theory[J].Journal of Central South University of Technology,2009,16(6):1001-1005.
[14]STERPIL D,CIVIDINI A.A physical and numerical investigation on the stability of shallow tunnels in strain softening media[J].Rock Mechanics and Rock Engineering,2004,37(4):277-298.
[15]ZARETSKIIL Y K,KARABAEVL M I,KHACHATURYAN N S.Construction monitoring of a shallow tunnel in the Lefortovo District of Moscow[J].Soil Mechanics and Foundation Engineering,2004,41(2):45-51.
[16]许增会,刘刚.地震区隧道稳定性分析方法[J].公路,2004,(10):189-193.XU Zeng-hui,LIU Gang.A study of stability analysis of tunnels in seismic region[J].Highway,2004,(10):189-193.
[17]刘晶波,李彬,刘祥庆.地下结构抗震设计中的静力弹塑性分析方法[J].土木工程学报,2007,47(7):68-76.LIU Jing-bo,LI Bin,LIU Xiang-qing.A static elasto-plastic analysis method in seismic design of underground structures[J].China Civil Engineering Journal,2007,47(7):68-76.
[18]程选生,郑颖人.地震作用下无衬砌黄土隧道围岩结构安全系数的计算探讨[J].岩土力学,2011,32(3):769-774.CHENG Xuan-sheng,ZHENG Ying-ren.Calculation discussion about safety factor of unlined loess tunnel wall rock structure under earthquake[J].Rock and Soil Mechanics,2011,32(3):769-774.
[19]谷兆祺,彭守拙,李仲奎.地下洞室工程[M].北京:清华大学出版社,1994.
[20]CHENG X S,TIAN R R,WANG J L.Parameter determination about loess tunnel analysis model under earthquake action[C]//Proceedings of the Eleventh International Symposium on Structural Engineering.Guangzhou City:Science Press,2010:34-38.
[21]陈立伟,彭建兵,范文,等.地震作用下黄土暗穴的稳定性[J].长安大学学报(自然科学版),2007,27(6):34-36.CHEN Li-wei,PENG Jian-bing,FAN Wen,et al.Stability of loess hidden hole under earthquake[J].Journal of Chang’an University(Natural Science Edition),2007,27(6):34-36.
[22]彭建兵,李庆春,陈志新,等.黄土洞穴灾害[M].北京:科学出版社,2008.
[23]王勖成,邵敏.有限单元法基本原理和数值方法[M].北京:清华大学出版社(第二版),2000.
[24]郑颖人,陈祖煜,王恭先,等.边坡与滑坡工程治理[M].北京:人民交通出版社,2007.
[25]郑颖人,赵尚毅,邓楚键,等.有限元极限分析法发展及其在岩土工程中的应用[J].中国工程科学,2006,8(12):39-61.ZHENG Ying-ren,ZHAO Shang-yi,DENG Chu-jian,et al.Development of finite element limit analysis method and its applications in geotechnical engineering[J].Engineering Sciences,2006,8(12):39-61.
[26]郑颖人,赵尚毅,张鲁渝.用有限元强度折减法进行边坡稳定分析[J].中国工程科学,2002,4(10):57-62.ZHNG Ying-ren,ZHAO Shang-yi,ZHANG Lu-yu.Slope stability analysis by strength reduction FEM[J].Engineering Science,2002,4(10):57-62.
[27]王峻,王兰民,李兰.永登5.8级地震中黄土震陷灾害的探讨[J].地震研究,2005,28(4):393-397.WANG Jun,WANG Lan-min,LI Lan.Discussion on the loess subsidence disaster caused by the Yongdeng M5.8 earthquake[J].Journal of Seimological Research,2005,28(4):393-397.
[28]中华人民共和国建设部.GB 50011-2001建筑抗震设计规范[S].北京:中国建筑工业出版社,2001.
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