大型地下洞室地震灾变过程三维动力有限元模拟
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摘要
地震作用是影响大型地下洞室群长期安全运行的主要外界因素。采用时程分析法模拟地震灾变中洞室围岩地震响应过程,是研究地下洞室抗震的一种有效方法。为此,开发地下洞室地震灾变三维动力有限元数值模拟系统。该系统采用显式中心差分法求解。为加快求解速度,对程序进行并行化处理并在积分方法上提出多高斯点分区混合积分法;考虑高应变率下材料的强化特性和循环荷载作用下围岩损伤特性,提出适用于地下洞室抗震分析的岩体动力本构模型;人工边界采用黏弹性边界;考虑地震波入射的方向性、多面性和非一致性,提出适用于地下洞室抗震分析的地震波空间斜入射法。通过计算通用数值分析软件的验证算例,表明该系统程序求解的正确性。同时,通过对鲁基场窑洞式地下厂房地震灾变时程模拟,表明系统程序在实际工程问题分析中的可靠性和实用性。
The earthquake impact is a major external factor influencing the long term stability of underground caverns.Time-history analysis method is able to simulate the earthquake response of surrounding rock in underground caverns during earthquake disaster process.It has been proved to be an effective method to analyze the aseismic issue of underground caverns.The numerical simulation system using three-dimensional dynamic finite element method is developed to study the earthquake disaster in underground caverns.Central difference method is employed in this system to solve the problem.To enhance the solving speed,parallel procedures and hybrid Gauss point integration method are proposed in programming.Strengthening features of materials under high strain rate and damage features of surrounding rock under cyclic loading are considered.The dynamic constitutive model for rock masses is presented.It is suitable for the aseismic analysis of underground caverns.Visco-elastic boundary is adopted in artificial boundary.The spatial oblique incident method which is suitable for the aseismic analysis of underground caverns is proposed.It is able to reflect the specific incident direction,the multi-incident surfaces and the inconsistency of seismic wave.An example is given to verify the correctness of the developed system by comparing its calculation results with common software's calculation results.A case study is then conducted to simulate the earthquake disaster process of the cave-typed underground caverns at Lujichang hydropower plant.The results derived from time-history analysis indicate the reliability and practicability of the developed system.
The earthquake impact is a major external factor influencing the long term stability of underground caverns.Time-history analysis method is able to simulate the earthquake response of surrounding rock in underground caverns during earthquake disaster process.It has been proved to be an effective method to analyze the aseismic issue of underground caverns.The numerical simulation system using three-dimensional dynamic finite element method is developed to study the earthquake disaster in underground caverns.Central difference method is employed in this system to solve the problem.To enhance the solving speed,parallel procedures and hybrid Gauss point integration method are proposed in programming.Strengthening features of materials under high strain rate and damage features of surrounding rock under cyclic loading are considered.The dynamic constitutive model for rock masses is presented.It is suitable for the aseismic analysis of underground caverns.Visco-elastic boundary is adopted in artificial boundary.The spatial oblique incident method which is suitable for the aseismic analysis of underground caverns is proposed.It is able to reflect the specific incident direction,the multi-incident surfaces and the inconsistency of seismic wave.An example is given to verify the correctness of the developed system by comparing its calculation results with common software's calculation results.A case study is then conducted to simulate the earthquake disaster process of the cave-typed underground caverns at Lujichang hydropower plant.The results derived from time-history analysis indicate the reliability and practicability of the developed system.
引文
[1]LIU J B,DU Y X,WANG Z Y,et al.3D viscous-spring artificial boundary in time domain[J].Earthquake Engineering and Engineering Vibration,2006,5(1):93-102.
[2]杜修力,赵密,王进挺.近场波动模拟的人工应力边界条件[J].力学学报,2006,38(1):49-56.(DU Xiuli,ZHAO Mi,WANG Jinting.A stress artificial boundary in FEA for near-field wave problem[J].Acta Mechanica Sinica,2006,38(1):49-56.(in Chinese))
[3]李小军,卢滔.水电站地下厂房洞室群地震反应显式有限元分析[J].水力发电学报,2009,28(5):41-46.(LI Xiaojun,LU Tao.Explicit finite element analysis of earthquake response for underground caverns of hydropower stations[J].Journal of Hydroelectric Engineering,2009,28(5):41-46.(in Chinese))
[4]张晓志,谢礼立.采用显式有限元方法求解开放系统动力响应的主要环节和问题[J].地震工程与工程振动,2005,25(2):10-15.(ZHANG Xiaozhi,XIE Lili.Problems in numerical solution of complex open system by using explicit finite element method[J].Earthquake Engineering and Engineering Vibration,2005,25(2):10-15.(in Chinese))
[5]钱七虎,戚承志.岩石、岩体的动力强度与动力破坏准则[J].同济大学学报(自然科学版),2008,36(12):1 599-1 605.(QIAN Qihu,QI Chengzhi.Dynamic strength and dynamic fracture criteria of rock and rock mass[J].Journal of Tongji University(Natural Science),2008,36(12):1 599-1 605.(in Chinese))
[6]戚承志,钱七虎.岩石等脆性材料动力强度依赖应变率的物理机制[J].岩石力学与工程学报,2003,22(2):177-181.(QI Chengzhi,QIAN Qihu.Physical mechanism of dependence of material strength on strain rate for rock-like material[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(2):177-181.(in Chinese))
[7]赵坚,李海波.莫尔-库仑和霍克-布朗强度准则用于评估脆性岩石动态强度的适用性[J].岩石力学与工程学报,2003,22(2):171-176.(ZHAO Jian,LI Haibo.Estimating the dynamic strength of brittle rock using Mohr-Coulomb and Hoek-Brown criteria[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(2):171-176.(in Chinese))
[8]李海波,朱莅,吕涛,等.考虑地震动空间非一致性的岩体地下洞室群地震反应分析[J].岩石力学与工程学报,2008,27(9):1 757-1 766.(LI Haibo,ZHU Li,LU Tao,et al.Dynamic response analysis of large underground excavations in jointed rock[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(9):1 757-1 766.(in Chinese))
[9]陈健云,胡志强,林皋.超大型地下洞室群的三维地震响应分析[J].岩土工程学报,2001,23(4):494-498.(CHEN Jianyun,HU Zhiqiang,LIN Gao.3D seismic response study on large scale underground group caverns[J].Chinese Journal of Geotechnical Engineering,2001,23(4):494-498.(in Chinese))
[10]张志国,肖明,张雨霆,等.大型地下洞室三维弹塑性损伤动力有限元分析[J].岩石力学与工程学报,2010,29(5):982-989.(ZHANG Zhiguo,XIAO Ming,ZHANG Yuting,et al.Dynamic finite element analysis of large-scale complex underground caverns with three-dimensional elastoplastic damage model[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(5):982-989.(in Chinese))
[11]张雄,王天舒.计算动力学[M].北京:清华大学出版社,2007.(ZHANG Xiong,WANG Tianshu.Computational dynamics[M].Beijing:Tsinghua University Press,2007.(in Chinese))
[12]陈育民,徐鼎平.FLAC/FLAC3D基础与工程实例[M].北京:中国水利水电出版社,2008.(CHEN Yumin,XU Dingping.Fundamentals of FLAC and FLAC3D and case study[M].Beijing:China Water Power Press,2008.(in Chinese))
[13]葛修润.周期荷载下岩石大型三轴试件的变形和强度特性研究[J].岩土力学,1987,8(2):11-19.(GE Xiurun.Study on deformation and strength behaviour of the large-scale triaxial rock samples under cyclic loading[J].Rock and Soil Mechanics,1987,8(2):11-19.(in Chinese))
[14]GRADY D E.Shock wave properties of brittle solids[C]//SCHMIDT S ed.Shock Compression of Condensed Matters.New York:AIP Press,1996:9-20.
[15]吴绵拔,刘远惠.中等应变速率对岩石力学特性的影响[J].岩土力学,1980,1(1):51-58.(WU Mianba,LIU Yuanhui.The effect of intermediate strain rates on mechanical properties of rock[J].Rock and Soil Mechanics,1980,1(1):51-58.(in Chinese))
[16]林皋,陈健云,肖诗云.混凝土的动力特性与拱坝的非线性地震响应[J].水利学报,2003,34(6):30-37.(LIN Gao,CHEN Jianyun,XIAO Shiyun.Dynamic behavior of concrete and nonlinear seismic response of arch dam[J].Journal of Hydraulic Engineering,2003,34(6):30-37.(in Chinese))
[17]李海波,赵坚,李廷芥.滑移型裂纹模型在研究岩石动态单轴抗压强度中的应用[J].岩石力学与工程学报,2001,20(3):315-319.(LI Haibo,ZHAO Jian,LI Tingjie.Study of dynamic uniaxial compressive strength of rock material using sliding crack model[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(3):315-319.(in Chinese))
[18]勒迈特J.损伤力学教程[M].倪金刚,陶春虎译.北京:科学出版社,1998.(LEMAITRE J.A course on damage mechanics[M].Translated by NI Jingang,TAO Chunhu.Beijing:Science Press,1998.(in Chinese))
[19]肖明.地下洞室围岩稳定与支护数值方法研究[博士学位论文][D].武汉:武汉大学,2002.(XIAO Ming.Study on numerical analysis method of stability and supporting for underground caverns[Ph.D.Thesis][D].Wuhan:Wuhan University,2002.(in Chinese))
[20]Itasca Consulting Group Inc..FLAC3D users'manual[R].Minneapolis:Itasca Consulting Group Inc.,2005.
[21]廖振鹏,周正华,张艳红.波动数值模拟中透射边界的稳定实现[J].地球物理学报,2002,45(4):533-544.(LIAO Zhenpeng,ZHOU Zhenghua,ZHANG Yanhong.Stable implementation of transmitting boundary in numerical simulation of wave motion[J].Chinese Journal of Geophysics,2002,45(4):533-544.(in Chinese))
[22]刘晶波,王振宇,杜修力,等.波动问题中的三维时域黏弹性人工边界[J].工程力学,2005,22(6):46-51.(LIU Jingbo,WANG Zhenyu,DU Xiuli,et al.Three-dimensional viscoelastic artificial boundaries in time domain for wave motion problems[J].Engineering Mechanics,2005,22(6):46-51.(in Chinese))
[23]杜修力,赵密.基于黏弹性边界的拱坝地震反应分析方法[J].水利学报,2006,37(9):1 063-1 069.(DU Xiuli,ZHAO Mi.Analysis method for seismic response of arch dams in time domain based on visco-elastic artificial boundary condition[J].Journal of Hydraulic Engineering,2006,37(9):1 063-1 069.(in Chinese))
[24]胡进军,谢礼立.地下地震动频谱特点研究[J].地震工程与工程振动,2004,24(6):1-8.(HU Jinjun,XIE Lili.Spectral characteristics of earthquake sub-ground motions[J].Earthquake Engineering and Engineering Vibration,2004,24(6):1-8.(in Chinese))
[25]中华人民共和国国家标准编写组.GB50011-2001建筑抗震设计规范[S].北京:中国标准出版社,2001.(The National Standards Compilation Group of People's Republic of China.GB 50011-2001 Code for seismic design of buildings[S].Beijing:Standards Press of China,2001.(in Chinese))
[26]中华人民共和国国家标准编写组.GB 17741-2005工程场地地震安全性评价技术规范[S].北京:中国标准出版社,2005.(The National Standards Compilation Group of People's Republic of China.GB 17741-2005 Evaluation of seismic safety for engineering sites[S].Beijing:Standards Press of China,2005.(in Chinese))
[2]杜修力,赵密,王进挺.近场波动模拟的人工应力边界条件[J].力学学报,2006,38(1):49-56.(DU Xiuli,ZHAO Mi,WANG Jinting.A stress artificial boundary in FEA for near-field wave problem[J].Acta Mechanica Sinica,2006,38(1):49-56.(in Chinese))
[3]李小军,卢滔.水电站地下厂房洞室群地震反应显式有限元分析[J].水力发电学报,2009,28(5):41-46.(LI Xiaojun,LU Tao.Explicit finite element analysis of earthquake response for underground caverns of hydropower stations[J].Journal of Hydroelectric Engineering,2009,28(5):41-46.(in Chinese))
[4]张晓志,谢礼立.采用显式有限元方法求解开放系统动力响应的主要环节和问题[J].地震工程与工程振动,2005,25(2):10-15.(ZHANG Xiaozhi,XIE Lili.Problems in numerical solution of complex open system by using explicit finite element method[J].Earthquake Engineering and Engineering Vibration,2005,25(2):10-15.(in Chinese))
[5]钱七虎,戚承志.岩石、岩体的动力强度与动力破坏准则[J].同济大学学报(自然科学版),2008,36(12):1 599-1 605.(QIAN Qihu,QI Chengzhi.Dynamic strength and dynamic fracture criteria of rock and rock mass[J].Journal of Tongji University(Natural Science),2008,36(12):1 599-1 605.(in Chinese))
[6]戚承志,钱七虎.岩石等脆性材料动力强度依赖应变率的物理机制[J].岩石力学与工程学报,2003,22(2):177-181.(QI Chengzhi,QIAN Qihu.Physical mechanism of dependence of material strength on strain rate for rock-like material[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(2):177-181.(in Chinese))
[7]赵坚,李海波.莫尔-库仑和霍克-布朗强度准则用于评估脆性岩石动态强度的适用性[J].岩石力学与工程学报,2003,22(2):171-176.(ZHAO Jian,LI Haibo.Estimating the dynamic strength of brittle rock using Mohr-Coulomb and Hoek-Brown criteria[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(2):171-176.(in Chinese))
[8]李海波,朱莅,吕涛,等.考虑地震动空间非一致性的岩体地下洞室群地震反应分析[J].岩石力学与工程学报,2008,27(9):1 757-1 766.(LI Haibo,ZHU Li,LU Tao,et al.Dynamic response analysis of large underground excavations in jointed rock[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(9):1 757-1 766.(in Chinese))
[9]陈健云,胡志强,林皋.超大型地下洞室群的三维地震响应分析[J].岩土工程学报,2001,23(4):494-498.(CHEN Jianyun,HU Zhiqiang,LIN Gao.3D seismic response study on large scale underground group caverns[J].Chinese Journal of Geotechnical Engineering,2001,23(4):494-498.(in Chinese))
[10]张志国,肖明,张雨霆,等.大型地下洞室三维弹塑性损伤动力有限元分析[J].岩石力学与工程学报,2010,29(5):982-989.(ZHANG Zhiguo,XIAO Ming,ZHANG Yuting,et al.Dynamic finite element analysis of large-scale complex underground caverns with three-dimensional elastoplastic damage model[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(5):982-989.(in Chinese))
[11]张雄,王天舒.计算动力学[M].北京:清华大学出版社,2007.(ZHANG Xiong,WANG Tianshu.Computational dynamics[M].Beijing:Tsinghua University Press,2007.(in Chinese))
[12]陈育民,徐鼎平.FLAC/FLAC3D基础与工程实例[M].北京:中国水利水电出版社,2008.(CHEN Yumin,XU Dingping.Fundamentals of FLAC and FLAC3D and case study[M].Beijing:China Water Power Press,2008.(in Chinese))
[13]葛修润.周期荷载下岩石大型三轴试件的变形和强度特性研究[J].岩土力学,1987,8(2):11-19.(GE Xiurun.Study on deformation and strength behaviour of the large-scale triaxial rock samples under cyclic loading[J].Rock and Soil Mechanics,1987,8(2):11-19.(in Chinese))
[14]GRADY D E.Shock wave properties of brittle solids[C]//SCHMIDT S ed.Shock Compression of Condensed Matters.New York:AIP Press,1996:9-20.
[15]吴绵拔,刘远惠.中等应变速率对岩石力学特性的影响[J].岩土力学,1980,1(1):51-58.(WU Mianba,LIU Yuanhui.The effect of intermediate strain rates on mechanical properties of rock[J].Rock and Soil Mechanics,1980,1(1):51-58.(in Chinese))
[16]林皋,陈健云,肖诗云.混凝土的动力特性与拱坝的非线性地震响应[J].水利学报,2003,34(6):30-37.(LIN Gao,CHEN Jianyun,XIAO Shiyun.Dynamic behavior of concrete and nonlinear seismic response of arch dam[J].Journal of Hydraulic Engineering,2003,34(6):30-37.(in Chinese))
[17]李海波,赵坚,李廷芥.滑移型裂纹模型在研究岩石动态单轴抗压强度中的应用[J].岩石力学与工程学报,2001,20(3):315-319.(LI Haibo,ZHAO Jian,LI Tingjie.Study of dynamic uniaxial compressive strength of rock material using sliding crack model[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(3):315-319.(in Chinese))
[18]勒迈特J.损伤力学教程[M].倪金刚,陶春虎译.北京:科学出版社,1998.(LEMAITRE J.A course on damage mechanics[M].Translated by NI Jingang,TAO Chunhu.Beijing:Science Press,1998.(in Chinese))
[19]肖明.地下洞室围岩稳定与支护数值方法研究[博士学位论文][D].武汉:武汉大学,2002.(XIAO Ming.Study on numerical analysis method of stability and supporting for underground caverns[Ph.D.Thesis][D].Wuhan:Wuhan University,2002.(in Chinese))
[20]Itasca Consulting Group Inc..FLAC3D users'manual[R].Minneapolis:Itasca Consulting Group Inc.,2005.
[21]廖振鹏,周正华,张艳红.波动数值模拟中透射边界的稳定实现[J].地球物理学报,2002,45(4):533-544.(LIAO Zhenpeng,ZHOU Zhenghua,ZHANG Yanhong.Stable implementation of transmitting boundary in numerical simulation of wave motion[J].Chinese Journal of Geophysics,2002,45(4):533-544.(in Chinese))
[22]刘晶波,王振宇,杜修力,等.波动问题中的三维时域黏弹性人工边界[J].工程力学,2005,22(6):46-51.(LIU Jingbo,WANG Zhenyu,DU Xiuli,et al.Three-dimensional viscoelastic artificial boundaries in time domain for wave motion problems[J].Engineering Mechanics,2005,22(6):46-51.(in Chinese))
[23]杜修力,赵密.基于黏弹性边界的拱坝地震反应分析方法[J].水利学报,2006,37(9):1 063-1 069.(DU Xiuli,ZHAO Mi.Analysis method for seismic response of arch dams in time domain based on visco-elastic artificial boundary condition[J].Journal of Hydraulic Engineering,2006,37(9):1 063-1 069.(in Chinese))
[24]胡进军,谢礼立.地下地震动频谱特点研究[J].地震工程与工程振动,2004,24(6):1-8.(HU Jinjun,XIE Lili.Spectral characteristics of earthquake sub-ground motions[J].Earthquake Engineering and Engineering Vibration,2004,24(6):1-8.(in Chinese))
[25]中华人民共和国国家标准编写组.GB50011-2001建筑抗震设计规范[S].北京:中国标准出版社,2001.(The National Standards Compilation Group of People's Republic of China.GB 50011-2001 Code for seismic design of buildings[S].Beijing:Standards Press of China,2001.(in Chinese))
[26]中华人民共和国国家标准编写组.GB 17741-2005工程场地地震安全性评价技术规范[S].北京:中国标准出版社,2005.(The National Standards Compilation Group of People's Republic of China.GB 17741-2005 Evaluation of seismic safety for engineering sites[S].Beijing:Standards Press of China,2005.(in Chinese))
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