基于逐步扩大网格法的饱和无限地基动力分析
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摘要
饱和无限地基的动力分析是研究结构与饱和土共同作用的基础。当用有限区域模拟饱和无限地基时,将在人工截取的边界上发生波的反射,导致模拟失真。该文基于远置人工边界的原理,采用逐步扩大网格法的思想来解决这一问题。并通过算例验证了该方法的精度。该方法避免了饱和介质中其他人工边界实施上的繁琐,并且避开了其它人工边界存在的大角度入射情况以及稳定性问题等不确定因素,可以用于饱和介质中其他人工边界条件的检验工作。
Dynamic analysis of infinite saturated foundation is required to study the saturated soil-structure interaction.If infinite saturated foundation is simulated by a finite region,wave reflection will take place on the artificial intercepted boundary.Adopting remote artificial boundaries,this problem is solved by gradual enlargement mesh.The method is verified through an example.With gradual enlargement mesh method,not only the difficulty of implementation on other artificial boundary can be avoided,but also some uncertain factors in other artificial boundary such as boundary stability and large angle incidence and so on can be avoided,so it can be used to check other artificial boundary.
Dynamic analysis of infinite saturated foundation is required to study the saturated soil-structure interaction.If infinite saturated foundation is simulated by a finite region,wave reflection will take place on the artificial intercepted boundary.Adopting remote artificial boundaries,this problem is solved by gradual enlargement mesh.The method is verified through an example.With gradual enlargement mesh method,not only the difficulty of implementation on other artificial boundary can be avoided,but also some uncertain factors in other artificial boundary such as boundary stability and large angle incidence and so on can be avoided,so it can be used to check other artificial boundary.
引文
[1]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:I.Low-frequency range[J].Journal of the Acoustical Society of American,1956,28(2):168―178.
[2]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:II.Higher frequency range[J].Journal of the Acoustical Society of American,1956,28(2):179―191.
[3]Biot M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33(4):1482―1498.
[4]Degrande G,De Roeck G.An absorbing boundary condition for wave propagation in saturated poroelastic media―Part I:Formulation and efficiency evaluation[J].Soil Dynamics and Earthquake Engineering,1993,12:411―421.
[5]Degrande G,De Roeck G.An absorbing boundary condition for wave propagation in saturated poroelastic media―Part II:Finite element formulation[J].Soil Dynamics and Earthquake Engineering,1993,12:423―432.
[6]Akiyoshi T,Sun X,Fuchida K.General absorbing boundary conditions for dynamic analysis of fluid-saturated porous media[J].Soil Dynamics and Earthquake Engineering,1998,17:397―406.
[7]吴德伦,张建华.饱和孔隙介质中波动分析的加权吸收边界条件[J].岩土工程学报,1997,19(4):57―65.Wu Delun,Zhang Jianhua.A weighted absorbing boundary for wave propagation in poroelastic media[J].Chinese Journal of Geotechnical Engineering,1997,19(14):57―65.(in Chinese)
[8]陈少林,廖振鹏.多次透射公式在衰减波场中的实现[J].地震学报,2003,25(3):272―279.Chen Shaolin,Liao Zhenpeng.Multi-transmitting Formula for Attenuating waves[J].Acta Seismologica Sinica,2003,25(3):272―279.(in Chinese)
[9]贺向丽,李同春.无限域波动问题的局部非协调网格法[J].振动工程学报,2006,19(1):124―127.He Xiangli,Li Tongchun.Local incompatible mesh method for infinite media wave problems[J].Journal of Vibration Engineering,2006,19(1):124―127.(in Chinese)
[10]贺向丽,李同春,任灏.基于逐步扩大网格法的重力坝地震响应分析[C].第17届全国结构工程学术会议,北京,2008.He Xiangli,Li Tongchun,Ren Hao.Analysis of seismic response for gravity dam based on gradual enlargement mesh method[C].Proceedings of the17th National Conference on Structural Engineering,Beijing,2008.(in Chinese)
[11]Zienkiewicz O C,Bettes P.Soil and other saturated media under transient,dynamic conditions:General formulation and the validity of various simplifying assumptions[M]//Pande G N,Zienkiewicz O C.Soil Mechanics Transient and Cyclilc Loads,New York:Wiley,1982:1―16.
[2]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:II.Higher frequency range[J].Journal of the Acoustical Society of American,1956,28(2):179―191.
[3]Biot M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33(4):1482―1498.
[4]Degrande G,De Roeck G.An absorbing boundary condition for wave propagation in saturated poroelastic media―Part I:Formulation and efficiency evaluation[J].Soil Dynamics and Earthquake Engineering,1993,12:411―421.
[5]Degrande G,De Roeck G.An absorbing boundary condition for wave propagation in saturated poroelastic media―Part II:Finite element formulation[J].Soil Dynamics and Earthquake Engineering,1993,12:423―432.
[6]Akiyoshi T,Sun X,Fuchida K.General absorbing boundary conditions for dynamic analysis of fluid-saturated porous media[J].Soil Dynamics and Earthquake Engineering,1998,17:397―406.
[7]吴德伦,张建华.饱和孔隙介质中波动分析的加权吸收边界条件[J].岩土工程学报,1997,19(4):57―65.Wu Delun,Zhang Jianhua.A weighted absorbing boundary for wave propagation in poroelastic media[J].Chinese Journal of Geotechnical Engineering,1997,19(14):57―65.(in Chinese)
[8]陈少林,廖振鹏.多次透射公式在衰减波场中的实现[J].地震学报,2003,25(3):272―279.Chen Shaolin,Liao Zhenpeng.Multi-transmitting Formula for Attenuating waves[J].Acta Seismologica Sinica,2003,25(3):272―279.(in Chinese)
[9]贺向丽,李同春.无限域波动问题的局部非协调网格法[J].振动工程学报,2006,19(1):124―127.He Xiangli,Li Tongchun.Local incompatible mesh method for infinite media wave problems[J].Journal of Vibration Engineering,2006,19(1):124―127.(in Chinese)
[10]贺向丽,李同春,任灏.基于逐步扩大网格法的重力坝地震响应分析[C].第17届全国结构工程学术会议,北京,2008.He Xiangli,Li Tongchun,Ren Hao.Analysis of seismic response for gravity dam based on gradual enlargement mesh method[C].Proceedings of the17th National Conference on Structural Engineering,Beijing,2008.(in Chinese)
[11]Zienkiewicz O C,Bettes P.Soil and other saturated media under transient,dynamic conditions:General formulation and the validity of various simplifying assumptions[M]//Pande G N,Zienkiewicz O C.Soil Mechanics Transient and Cyclilc Loads,New York:Wiley,1982:1―16.
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