基于静动力有限元的边坡抗震稳定分析方法
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摘要
由人工截断边界输入地震波,通过时程积分法确定地震荷载作用下边坡的应力和变形,在人工截断边界上采用黏-弹性人工边界条件模拟地基辐射阻尼的影响。采用有限元强度折减法求解边坡稳定安全系数,以塑性区贯通时刻特征点的位移突变作为边坡失稳的评判标准。非线性有限元和黏-弹性人工边界条件结合运用,建立了基于静动力有限元的边坡抗震稳定分析方法。该方法在稳定安全系数的定义上和传统的刚体极限平衡法是一致的。以十里铺水电站为工程实例,分析了库区边坡的抗震稳定性,得出了边坡动力位移时程和动力稳定安全系数,计算结果合理评价了实际工程在地震荷载下的稳定性。
The seismic wave is input through artificial truncated boundaries,and the stress and deformation of the slope induced by seismic loading are determined by time-integration method.The effect of foundation radiation damping is simulated by adopting viscoelastic artificial boundaries condition on artificial truncated boundaries.Safety factor of slope stability is solved by finite elements strength reduction method.The displacement saltation of feature points when the connection of plastic zone occurs is considered as an instability criterion of the slope.The slope aseismic stability analysis method based on static and dynamic finite elements is put forward through combining the dynamic finite element method with the viscoelastic artificial boundaries conditions.On the definition of safety factor,the method is consistent with the traditional grid limit equilibrium method.Finally,taking Shilipu Hydropower Station for example,the slope dynamic stability of the reservoir slope is analyzed;and the time history of the slope dynamic displacements and the safety factor of dynamic stability are obtained.The calculation results agree very well with geological survey and are close to the actual situation,so as to indicate that the method can be used to evaluate dynamic stability of the practical engineering.
The seismic wave is input through artificial truncated boundaries,and the stress and deformation of the slope induced by seismic loading are determined by time-integration method.The effect of foundation radiation damping is simulated by adopting viscoelastic artificial boundaries condition on artificial truncated boundaries.Safety factor of slope stability is solved by finite elements strength reduction method.The displacement saltation of feature points when the connection of plastic zone occurs is considered as an instability criterion of the slope.The slope aseismic stability analysis method based on static and dynamic finite elements is put forward through combining the dynamic finite element method with the viscoelastic artificial boundaries conditions.On the definition of safety factor,the method is consistent with the traditional grid limit equilibrium method.Finally,taking Shilipu Hydropower Station for example,the slope dynamic stability of the reservoir slope is analyzed;and the time history of the slope dynamic displacements and the safety factor of dynamic stability are obtained.The calculation results agree very well with geological survey and are close to the actual situation,so as to indicate that the method can be used to evaluate dynamic stability of the practical engineering.
引文
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[2]刘立平,雷尊宇,周富春.地震边坡稳定分析方法综述[J].重庆交通学院学报,2001,20(3):83-88.LIU Li-ping,LEI Zun-yu,ZHOU Fu-chun.The evaluation of seismic slope stability analysis methods[J].Journal of Chongqing Jiaotong University,2001,20(3):83-88.
[3]TERZAGHI K.Mechanisms of landslides,engineering geology(Berdey)volume[M].US:Geological Society of America,1950.
[4]WU X Y,LAW K T.SELVADURAI,A P S.Examination of the pseudo static limit equilibrium method of dynamic stability analysis of slopes[C]//Proceedings of 44th Canadian Geotechnical Conference.Calgary:[s.n.].1991.
[5]ITO H,SATO K,SAWADA Y.Consideration on the seismic method and the design seismic coefficient of large cut slope under the strong earthquake[C]//Proceedings of International Congress on Rock Mechanics.Japan:[s.n.],1995:413-416.
[6]何蕴龙,陆述远.岩石边坡地震作用近似计算方法[J].岩土工程学报,1998,20(2):66-68.HE Yun-long,LU Shu-yuan.A method for calculating the seismic action in rock slope[J].Chinese Journal of Geotechnical Engineering,1998,20(2):66-68.
[7]唐洪祥,邵龙潭.地震动力作用下有限元土石坝边坡稳定性分析[J].岩石力学与工程学报,2004,3(8):1318-1324.TANG Hong-xiang,SHAO Long-tan.Finite element analysis of slope stability of earth-rock dam under earthquake[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(8):1318-1324.
[8]薄景山,徐国栋,景立平.土边坡地震反应及其动力稳定性分析[J].地震工程与工程振动,2001,21(2):116-120.BO Jing-shan,XU Guo-dong,JING Li-ping.Seismic response and dynamic stability analysis of soil slopes[J].Earthquake Engineering and Engineering Vibration,2001,21(1):116-120.
[9]周桂云,李同春.饱和-非饱和非稳定身流作用下岩质边坡稳定性分析[J].水电能源科学,2006,24(5):79-82.ZHOU Gui-yun,LI Tong-chun.Rocky slope stability analysis taking into account saturated-unsaturated seepage flow[J].Water Resources and Power,2006,24(5):79-82.
[10]沈聚敏.抗震工程学[M].北京:中国建筑工业出版社,2000.
[11]贺向丽,李同春.无限域中的动力人工边界条件[J].水利水电科技进展,2005,25(3):64-67.HE Xiang-li,LI Tong-chun.Dynamic artificial boundaries condition for infinite domain[J].Advance in Science and Technology of Water Resources,2005,25(3):64-67.
[12]CLAYTON R,ENGQUIST B.Absorbing boundary conditions for acoustic and elastic wave equations[J].Bulletin of the Seismological Society of America,1977,76:1529-1540.
[13]CLAYTON R,ENGQUIST B.Absorbing boundary conditions for wave-equation migration[J].Geophysics,1980,45:895-904.
[14]钱家欢,殷宗泽.土工原理与计算(第二版)[M].北京:中国水利水电出版社,1996.
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