SH波作用下岩质边坡响应规律的解析探讨
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摘要
基于弹性力学理论,推导了弹性波动方程,并给出了位移势函数的表达式。根据应力波传播理论建立了边坡中应力波传播模型,以SH波为例详细说明了边坡中不同部位的应力波叠加情况。将边坡的坡面和坡顶自由面解耦为2个相互独立的自由面,分别分析了2个自由面附近应力波场的叠加,并据此研究了边坡中波函数幅值变化情况,得到了边坡水平向动力放大规律和垂直向动力放大规律,以及这些规律产生周期性变化所满足的条件。
This paper develops a model about stress waves propagation in rock slope body according to the theory of stress waves propagation.Based on the theories of elasticity,it derives the elastic-dynamics equations and potential functions.Taking SH wave propagation as an example,the stress waves superposition at different parts of the slope is discussed.The sloping surface and slope crest are departed into two independent free surfaces.They do not affect each other in the process of reflecting stress waves.The stress waves superposition beside the two free surfaces are analyzed respectively.The amplitude of the superposed wave is discussed.It reveals the rules of both vertical and horizontal dynamic response amplifications of the slope.The rule for the vertical dynamic response amplification is that getting closer to slope surface,the particles' oscillation amplitude increase.The rule for the horizontal dynamic response amplification is that near slope crest,the particles' oscillation response increases,and reaches to the largest at slope crest.The condition for the two rules being cyclic variation is that the slope height is larger than 1/4 wavelength of SH wave.
This paper develops a model about stress waves propagation in rock slope body according to the theory of stress waves propagation.Based on the theories of elasticity,it derives the elastic-dynamics equations and potential functions.Taking SH wave propagation as an example,the stress waves superposition at different parts of the slope is discussed.The sloping surface and slope crest are departed into two independent free surfaces.They do not affect each other in the process of reflecting stress waves.The stress waves superposition beside the two free surfaces are analyzed respectively.The amplitude of the superposed wave is discussed.It reveals the rules of both vertical and horizontal dynamic response amplifications of the slope.The rule for the vertical dynamic response amplification is that getting closer to slope surface,the particles' oscillation amplitude increase.The rule for the horizontal dynamic response amplification is that near slope crest,the particles' oscillation response increases,and reaches to the largest at slope crest.The condition for the two rules being cyclic variation is that the slope height is larger than 1/4 wavelength of SH wave.
引文
[1]王存玉,王思敬.地震条件下二滩水库岸坡稳定性研究[A].见:岩体工程地质力学问题(七)[C].北京:科学出版社,1987,65～74.Wang Cunyu,Wang Sijing.Study on stability of the bank slope ofErtan reservoir under seismic condition.In:Problem of RockmassEngineering Geomechanics(Ⅶ),Beijing:Science Press,1987,65～74.
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[3]Qi Shengwen,Wu Faquan,Sun Jingzhong.General regularity of dy-namic response of slopes under dynamic input.Science in China(Series E).2003,46(Suppl.),120～132.
[4]祁生文.单面边坡的两种动力反应形式及其临界高度[J].地球物理学报,2006,49(2):518～523.Qi Shengwen.Two patterns of dynamic responses of sigle-free-surface slopes and their threshold height.Chinese Journal of Geo-physics,2006,49(2):518～523.
[5]徐光兴,姚令侃,高召宁,李朝红.边坡动力特性与动力响应的大型振动台模型试验研究[J].岩石力学与工程学报,2008,27(3):624～632.Xu Guangxing,Yao Lingkan,Gao Zhaoning,Li Zhaohong.Large-scale shaking table model test on the dynamic characteristics andseismic responses of slope.Chinese Journal of Rock Mechanics andEngineering,2008,27(3):624～632.
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[9]Jacques Ingles,JoséDarrozes,Jean-Claude Soula.Effects of thevertical component of ground shaking on earthquake-induced land-slide displacements using generalized Newmark analysis.Engineering Geology,2006,86:134～147.
[10]刘汉龙,费康,高玉峰.边坡地震稳定性时程分析方法[J].岩土力学,2003,24(4):553～557.Liu Hanlong,Fei Kuang,Gao Yufeng.Time history analysis methodof slope seismic stability.Rock and Soil Mechanics,2003,24(4):553～557.
[11]车伟,罗奇峰.复杂地形条件下地震波的传播研究[J].岩土工程学报,2008,30(9):1333～1337.Che Wei,Luo Qifeng.Seismic wave propagation in complex topog-raphy.Chinese Journal of Geotechnical and Engineering,2008,30(9):1333～1337.
[12]陆万明,罗学富.弹性理论基础(下册)(第二版)[M].北京:清华大学出版社,2001.Lu Wanming,Luo Xuefu.Basic Theory of Elasticity(2)(The Sec-ond Edition)[M].Beijing:Tsinghua University Press,2001.
[13]牛滨华,孙晟,孙春岩.位移位函数地震波在界面的广义散射[M].北京:地质出版社,2008.Niu Binhua,Sun Sheng,Sun Chunyan.The GeneralizedScattering of Seismic Waves in the Interface Based onDisplacement Function[M].Beijing:Geological PublishingHouse,2008.
[2]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 Yunlong,Lu Shuyuan.A method for calculation the seismic ac-tion in rock slope.Chinese Journal of Geotechnical Engineering,1998,20(2):66～68.
[3]Qi Shengwen,Wu Faquan,Sun Jingzhong.General regularity of dy-namic response of slopes under dynamic input.Science in China(Series E).2003,46(Suppl.),120～132.
[4]祁生文.单面边坡的两种动力反应形式及其临界高度[J].地球物理学报,2006,49(2):518～523.Qi Shengwen.Two patterns of dynamic responses of sigle-free-surface slopes and their threshold height.Chinese Journal of Geo-physics,2006,49(2):518～523.
[5]徐光兴,姚令侃,高召宁,李朝红.边坡动力特性与动力响应的大型振动台模型试验研究[J].岩石力学与工程学报,2008,27(3):624～632.Xu Guangxing,Yao Lingkan,Gao Zhaoning,Li Zhaohong.Large-scale shaking table model test on the dynamic characteristics andseismic responses of slope.Chinese Journal of Rock Mechanics andEngineering,2008,27(3):624～632.
[6]AJ Li,AV Lyamin,RS Merifield.Seismic rock slope stability chartsbased on limit analysis methods.Computers and Geotechnics,2009,36:135～148.
[7]George D Bouckovalas,Achilleas G Papadimitriou.Numerical eval-uation of slope topography effects on seismic ground motion.SoilDynamic and Earthquake Engineering,2005,25:547～558.
[8]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,2004,23(8):1318～1324.Tang Hongxiang,Shao Longtan.Finite element analysis on slopestability of earth～rock dam under earthquake.Chinese Journal ofRock Mechanics and Engineering,2004,23(8):1318～1324.
[9]Jacques Ingles,JoséDarrozes,Jean-Claude Soula.Effects of thevertical component of ground shaking on earthquake-induced land-slide displacements using generalized Newmark analysis.Engineering Geology,2006,86:134～147.
[10]刘汉龙,费康,高玉峰.边坡地震稳定性时程分析方法[J].岩土力学,2003,24(4):553～557.Liu Hanlong,Fei Kuang,Gao Yufeng.Time history analysis methodof slope seismic stability.Rock and Soil Mechanics,2003,24(4):553～557.
[11]车伟,罗奇峰.复杂地形条件下地震波的传播研究[J].岩土工程学报,2008,30(9):1333～1337.Che Wei,Luo Qifeng.Seismic wave propagation in complex topog-raphy.Chinese Journal of Geotechnical and Engineering,2008,30(9):1333～1337.
[12]陆万明,罗学富.弹性理论基础(下册)(第二版)[M].北京:清华大学出版社,2001.Lu Wanming,Luo Xuefu.Basic Theory of Elasticity(2)(The Sec-ond Edition)[M].Beijing:Tsinghua University Press,2001.
[13]牛滨华,孙晟,孙春岩.位移位函数地震波在界面的广义散射[M].北京:地质出版社,2008.Niu Binhua,Sun Sheng,Sun Chunyan.The GeneralizedScattering of Seismic Waves in the Interface Based onDisplacement Function[M].Beijing:Geological PublishingHouse,2008.
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