岩石边坡动力稳定安全系数的块体单元法分析
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摘要
将动力分析的块体单元法应用于岩石边坡地震稳定时程分析。将黏弹性人工边界条件的思想与块体单元理论相结合,建立块体系统的人工边界条件,用以模拟地基的弹性恢复能力和地基对散射波能量的吸收,从而消除波动在计算区域边界上的反射。黏弹性边界具有稳定性好,易于与计算程序结合的优点。通过动力计算所得的块体加速度计算块体的惯性力,并由此判断块体可能的滑动模式,进而根据滑动模式将惯性力分解为块体滑动力和垂直于滑动方向的作用力,由此作用力计算块体的抗滑力。块体抗滑稳定安全系数即为抗滑力与滑动力之比,从而可以得到地震过程中块体稳定安全系数时程曲线。小湾水电站进水口边坡算例体现了该方法的工程应用能力。
Block element method(BEM) for dynamic analysis is developed and applied to historical analysis of seismic stability of rock slope. Combining the idea of viscoelastic boundary with the theory of BEM,the artificial boundary condition of BEM is formulated,which can eliminate the reflection of the seismic waves on the boundaries of the computational domain. Viscoelastic boundary has the merits of numerical stability and convenience to integrate with computational program. The inertial force of rock block is firstly computed by its acceleration obtained by dynamic analysis,then is decomposed according to supposed sliding mode into sliding force and force perpendicular to the supposed sliding direction,which is used for calculating resistance force. The factor of safety against sliding is defined by the ratio of the resistance force to the sliding force. When the seismic process finishes,the time-history curve of factor of safety against sliding of rock block can be obtained. The application of the intake slope of Xiaowan Hydropower Station demonstrates the capacity of this method.
Block element method(BEM) for dynamic analysis is developed and applied to historical analysis of seismic stability of rock slope. Combining the idea of viscoelastic boundary with the theory of BEM,the artificial boundary condition of BEM is formulated,which can eliminate the reflection of the seismic waves on the boundaries of the computational domain. Viscoelastic boundary has the merits of numerical stability and convenience to integrate with computational program. The inertial force of rock block is firstly computed by its acceleration obtained by dynamic analysis,then is decomposed according to supposed sliding mode into sliding force and force perpendicular to the supposed sliding direction,which is used for calculating resistance force. The factor of safety against sliding is defined by the ratio of the resistance force to the sliding force. When the seismic process finishes,the time-history curve of factor of safety against sliding of rock block can be obtained. The application of the intake slope of Xiaowan Hydropower Station demonstrates the capacity of this method.
引文
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[16]张国新,王光纶,裴觉民.基于流形方法的结构体破坏分析[J].岩石力学与工程学报,2001,20(3):281–287.(ZHANG Guoxin,WANG Guanglun,PEI Juemin.Structural failure analysis based on manifold method[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(3):281–287.(in Chinese))
[17]陈胜宏,强晟,陈尚法.加锚岩体的三维复合单元模型研究[J].岩石力学与工程学报,2003,22(1):1–8.(CHEN Shenghong,QIANG Sheng,CHEN Shangfa.Study on the three-dimensional composite element model of bolted rock masses[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(1):1–8.(in Chinese))
[18]CHEN S H,XU Q,HU J.Composite element method for seepage analysis of geotechnical structures with drainage hole array[J].Journal of Hydrodynamics(Series B),2004,16(3):260–266.
[19]CHEN S H,QIANG S.Composite element model for discontinuous rock masses[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(5):865–870.
[20]强晟,陈胜宏.不连续岩体的三维弹黏塑性复合单元模型研究[J].岩石力学与工程学报,2004,23(20):3390–3396.(QIANG Sheng,CHEN Shenghong.Three-dimensional elasto-viscoplastic composite element model of discontinuous rock masses[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(20):3390–3396.(in Chinese))
[21]陈胜宏.高坝复杂岩石地基及岩石高边坡稳定分析[M].北京:中国水利水电出版社,2002.(CHEN Shenghong.Stability analysis of complicated rock foundation of high dam and rock high slope[M].Beijing:China Water Power Press,2002.(in Chinese))
[22]郑惠峰,汪卫明,陈胜宏.块体单元法动力分析研究[J].岩石力学与工程学报,2007,26(3):608–613.(ZHENG Huifeng,WANG Weiming,CHEN Shenghong.Study on block element method for dynamic analysis[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(3):608–613.(in Chinese))
[23]LYSMER J,KULEMEYER R L.Finite dynamic model for infinite media[J].Journal of the Engineering Mechanics Division,ASCE,1969,95(4):859–877.
[24]DEEKS A J,RANDOLPH M F.Axisymmetric time-domain transmitting boundaries[J].Journal of the Engineering Mechanics Division,ASCE,1994,120(1):25–42.
[25]刘晶波,吕彦东.结构–地基动力相互作用问题分析的一种直接方法[J].土木工程学报,1998,31(3):55–64.(LIU Jingbo,LU Yandong.A direct method for analysis of dynamic soil-structure interaction[J].China Civil Engineering Journal,1998,31(3):55–64.(in Chinese))
[26]杜修力.局部解耦的时域波分析方法[J].世界地震工程,2000,16(3):22–26.(DU Xiuli.A partially decoupling analytical method for wave propagation problems in time domain[J].World Information on Earthquake Engineering,2000,16(3):22–26.(in Chinese))
[27]赵密.黏弹性人工边界及其与透射人工边界的比较研究[硕士学位论文][D].北京:北京工业大学,2004.(ZHAO Mi.Study on viscoelastic artificial boundary and its comparison with transmitting artificial boundary[M.S.Thesis][D].Beijing:Beijing University of Technology,2004.(in Chinese))
[28]艾龙根,舒胡毕.弹性动力学,第二卷:线性理论[M].戈革译.北京:石油工业出版社,1984.(ERINGEN A C,SUHUBI E S.Elastic dynamic mechanics,2nd volume:linear theory[M].Translated by GE Ge.Beijing:Petroleum Industry Press,1984.(in Chinese))
[29]徐明毅,汪卫明,陈胜宏.岩石边坡的危险滑动块体组合研究[J].岩土力学,2000,21(2):148–151.(XU Mingyi,WANG Weiming,CHEN Shenghong.Research on the dangerous sliding-block combination of rock slopes[J].Rock and Soil Mechanics,2000,21(2):148–151.(in Chinese))
[2]王毓泰,周维垣,毛健全,等.拱坝坝肩块体稳定分析[M].贵阳:贵州人民出版社,1982.(WANG Shutai,ZHOU Weiyuan,MAO Jianquan,et al.Stability analysis for block on arch dam abutment[M].Guiyang:Guizhou People′s Publishing House,1982.(in Chinese))
[3]HOVLAND H J.Three-dimensional slope stability analysis method[J].Journal of the Geotechnical Engineering Division,ASCE,1977,103(GT9):971–986.
[4]LAM L,FREDLUND D G.A general limit equilibrium model for three-dimensional slope stability analysis[J].Canadian Geotechnical Journal,1993,30(4):905–919.
[5]张伯艳,陈厚群,杜修力,等.拱坝坝肩抗震稳定分析[J].水利学报,2000,(11):55–59.(ZHANG Boyan,CHEN Houqun,DU Xiuli,et al.Arch dam abutment asiesmatic stability analysis[J].Journal of Hydraulic Engineering,2000,(11):55–59.(in Chinese))
[6]张伯艳,陈厚群.用有限元和刚体极限平衡方法分析坝肩抗震稳定[J].岩石力学与工程学报,2001,20(5):665–670.(ZHANG Boyan,CHEN Houqun.Analysis of abutment aseismatic stability by using finite element and rigid body limit equilibrium method[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(5):665–670.(in Chinese))
[7]CUNDALL P A.A computer model for simulating progressive large scale movement in blocky system[C]//Proceedings of the Symposium of the International Society of Rock Mechanics.Nancy,France:[s.n.],1971:11–18.
[8]王泳嘉,刑纪波.离散单元法及其在岩土力学中的应用[M].沈阳:东北工学院出版社,1991.(WANG Yongjia,XING Jibo.Distinct element method and its application to geotechnical engineering[M].Shengyang:Northeast Institute of Technology Press,1991.(in Chinese))
[9]ZHANG C,PEKAU O A,JIN F,et al.Application of distinct element method in dynamic analysis of high rock slopes and blocky structures[J].Soil Dynamic and Earthquake Engineering,1997,16(6):385–394.
[10]KAWAI T.A new discrete model for analysis of soil mechanics problem[J].Seisan KenKyn,1977,29(4):208–210.
[11]方义琳,卓家寿,章青.具有任意形状单元离散模型的界面元法[J].工程力学,1998,15(2):27–37.(FANG Yilin,ZHUO Jiashou,ZHANG Qing.Interface stress element method for distinct model with elements of arbitrary shape[J].Engineering Mechanics,1998,15(2):27–37.(in Chinese))
[12]Shi G H.Block system modeling by discontinuous deformation analysis[M].Southampton,UK:Computational Mechanics Publications,1993.
[13]王如路,陈乃明,刘宝琛.三维块体不连续变形分析理论简析[J].岩石力学与工程学报,1996,15(3):219–224.(WANG Rulu,CHEN Naiming,LIU Baochen.Study on the theory of three-dimensional block discontinuous deformation analysis[J].Chinese Journal of Rock Mechanics and Engineering,1996,15(3):219–224.(in Chinese))
[14]石根华.数值流形方法与非连续变形分析[M].裴觉民译.北京:清华大学出版社,1997.(SHI Genhua.Manifold method and discontinuous deformation analysis[M].Translates by PEI Juemin.Beijing:Tsinghua University Press,1997.(in Chinese))
[15]周维垣,杨若琼,剡公瑞.流形元法及其在工程中的应用[J].岩石力学与工程学报,1996,15(3):211–218.(ZHOU Weiyan,YANG Ruoqiong,YAN Gongrui.Manifold method and its application to engineering problems[J].Chinese Journal of Rock Mechanics and Engineering,1996,15(3):211–218.(in Chinese))
[16]张国新,王光纶,裴觉民.基于流形方法的结构体破坏分析[J].岩石力学与工程学报,2001,20(3):281–287.(ZHANG Guoxin,WANG Guanglun,PEI Juemin.Structural failure analysis based on manifold method[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(3):281–287.(in Chinese))
[17]陈胜宏,强晟,陈尚法.加锚岩体的三维复合单元模型研究[J].岩石力学与工程学报,2003,22(1):1–8.(CHEN Shenghong,QIANG Sheng,CHEN Shangfa.Study on the three-dimensional composite element model of bolted rock masses[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(1):1–8.(in Chinese))
[18]CHEN S H,XU Q,HU J.Composite element method for seepage analysis of geotechnical structures with drainage hole array[J].Journal of Hydrodynamics(Series B),2004,16(3):260–266.
[19]CHEN S H,QIANG S.Composite element model for discontinuous rock masses[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(5):865–870.
[20]强晟,陈胜宏.不连续岩体的三维弹黏塑性复合单元模型研究[J].岩石力学与工程学报,2004,23(20):3390–3396.(QIANG Sheng,CHEN Shenghong.Three-dimensional elasto-viscoplastic composite element model of discontinuous rock masses[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(20):3390–3396.(in Chinese))
[21]陈胜宏.高坝复杂岩石地基及岩石高边坡稳定分析[M].北京:中国水利水电出版社,2002.(CHEN Shenghong.Stability analysis of complicated rock foundation of high dam and rock high slope[M].Beijing:China Water Power Press,2002.(in Chinese))
[22]郑惠峰,汪卫明,陈胜宏.块体单元法动力分析研究[J].岩石力学与工程学报,2007,26(3):608–613.(ZHENG Huifeng,WANG Weiming,CHEN Shenghong.Study on block element method for dynamic analysis[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(3):608–613.(in Chinese))
[23]LYSMER J,KULEMEYER R L.Finite dynamic model for infinite media[J].Journal of the Engineering Mechanics Division,ASCE,1969,95(4):859–877.
[24]DEEKS A J,RANDOLPH M F.Axisymmetric time-domain transmitting boundaries[J].Journal of the Engineering Mechanics Division,ASCE,1994,120(1):25–42.
[25]刘晶波,吕彦东.结构–地基动力相互作用问题分析的一种直接方法[J].土木工程学报,1998,31(3):55–64.(LIU Jingbo,LU Yandong.A direct method for analysis of dynamic soil-structure interaction[J].China Civil Engineering Journal,1998,31(3):55–64.(in Chinese))
[26]杜修力.局部解耦的时域波分析方法[J].世界地震工程,2000,16(3):22–26.(DU Xiuli.A partially decoupling analytical method for wave propagation problems in time domain[J].World Information on Earthquake Engineering,2000,16(3):22–26.(in Chinese))
[27]赵密.黏弹性人工边界及其与透射人工边界的比较研究[硕士学位论文][D].北京:北京工业大学,2004.(ZHAO Mi.Study on viscoelastic artificial boundary and its comparison with transmitting artificial boundary[M.S.Thesis][D].Beijing:Beijing University of Technology,2004.(in Chinese))
[28]艾龙根,舒胡毕.弹性动力学,第二卷:线性理论[M].戈革译.北京:石油工业出版社,1984.(ERINGEN A C,SUHUBI E S.Elastic dynamic mechanics,2nd volume:linear theory[M].Translated by GE Ge.Beijing:Petroleum Industry Press,1984.(in Chinese))
[29]徐明毅,汪卫明,陈胜宏.岩石边坡的危险滑动块体组合研究[J].岩土力学,2000,21(2):148–151.(XU Mingyi,WANG Weiming,CHEN Shenghong.Research on the dangerous sliding-block combination of rock slopes[J].Rock and Soil Mechanics,2000,21(2):148–151.(in Chinese))
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