饱和地基上基础动力刚度的分析
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摘要
动力基础设计以及土-结构动力相互作用子结构分析方法中,确定基础动力刚度是其中的关键问题。实际工程中,有时需要考虑饱和地基情形。由于饱和地基上基础动力刚度求解问题的复杂性,往往需要通过数值方法进行求解。本文将基础动力刚度的一种时域求解方法推广到饱和地基情形,对饱和地基上基础动力刚度进行了分析。具体工作如下:
(1)将基础动力刚度的一种时域求解方法推广到饱和地基情形,并编制程序加以实现。通过给基础输入脉冲位移,应用集中质量显式有限元方法结合局部透射人工边界,得到饱和地基对基础的反力时程,然后应用FFT求得基础动力刚度。
(2)对均质饱和弹性半空间上明置基础和埋置基础的动力刚度进行了计算,讨论了计算中的相关问题。对泊松比、孔隙比和渗透系数对动力刚度的影响进行了分析。
(3)通过理论分析和算例验证,孔隙比和液相压缩模量取为零时,饱和地基情形的动力刚度将退化为一般弹性土情形的动力刚度。据此,实现了一般弹性土和饱和弹性土交错成层时动力刚度的求解,并分析了饱和弹性半空间上覆一般弹性土层时明置基础和埋置基础的动力刚度。分析了上覆弹性土层的层厚和基础埋深对动力刚度的影响。
(4)最后,对本文工作进行了总结,并给出了进一步研究的建议。
It is important to calculate the impedance matrix of foundations in dynamic foundation design and the substructure analysis of the soil-structure interaction.The impedance matrix of foundations on fluid-filled poro-elastic medium, complicated and difficult to resolve using analytical methods, is much concerned in engineering in last decades. In this thesis, a time domain solution method of impedance matrix of foundations on fluid-filled poro-elastic medium was provided. The work was as follows:
(1) Based on theory of wave propagation and the method of lumped-mass explicit finite element and local transmitting artificial boundary, an efficient time domain method of impedance matrix of foundations on fluid-filled poro-elastic medium is introduced and the corresponding program was programmed.
(2) The numerical analysis of impedance functions of surface and embedded foundations on homogeneous fluid-filled poro-elastic medium half-space was given. Parameters (Poisson ratio, void ratio and permeability coefficient) which effect impedance functions were discussed by the examples.
(3) When the values of void ratio and the modulus in compression of fluid phase are zero, the impedance matrix of foundation on fluid-filled poro-elastic soil will be reduced to that of foundation on elastic soil. In this way, the impedance matrix of foundations on the layered stratum which consists of the fluid-filled poro-elastic medium and the elastic medium can be resolved. The numerical analysis of impedance functions of surface and embedded foundations on elastic soil placed on the fluid-filled poro-elastic half-space were done and the effect of elastic soil thickness and the embedded depth on impedance were investigated.
(4) Finally, works in this paper were summarized and suggestions on further research were given.
(1)将基础动力刚度的一种时域求解方法推广到饱和地基情形,并编制程序加以实现。通过给基础输入脉冲位移,应用集中质量显式有限元方法结合局部透射人工边界,得到饱和地基对基础的反力时程,然后应用FFT求得基础动力刚度。
(2)对均质饱和弹性半空间上明置基础和埋置基础的动力刚度进行了计算,讨论了计算中的相关问题。对泊松比、孔隙比和渗透系数对动力刚度的影响进行了分析。
(3)通过理论分析和算例验证,孔隙比和液相压缩模量取为零时,饱和地基情形的动力刚度将退化为一般弹性土情形的动力刚度。据此,实现了一般弹性土和饱和弹性土交错成层时动力刚度的求解,并分析了饱和弹性半空间上覆一般弹性土层时明置基础和埋置基础的动力刚度。分析了上覆弹性土层的层厚和基础埋深对动力刚度的影响。
(4)最后,对本文工作进行了总结,并给出了进一步研究的建议。
It is important to calculate the impedance matrix of foundations in dynamic foundation design and the substructure analysis of the soil-structure interaction.The impedance matrix of foundations on fluid-filled poro-elastic medium, complicated and difficult to resolve using analytical methods, is much concerned in engineering in last decades. In this thesis, a time domain solution method of impedance matrix of foundations on fluid-filled poro-elastic medium was provided. The work was as follows:
(1) Based on theory of wave propagation and the method of lumped-mass explicit finite element and local transmitting artificial boundary, an efficient time domain method of impedance matrix of foundations on fluid-filled poro-elastic medium is introduced and the corresponding program was programmed.
(2) The numerical analysis of impedance functions of surface and embedded foundations on homogeneous fluid-filled poro-elastic medium half-space was given. Parameters (Poisson ratio, void ratio and permeability coefficient) which effect impedance functions were discussed by the examples.
(3) When the values of void ratio and the modulus in compression of fluid phase are zero, the impedance matrix of foundation on fluid-filled poro-elastic soil will be reduced to that of foundation on elastic soil. In this way, the impedance matrix of foundations on the layered stratum which consists of the fluid-filled poro-elastic medium and the elastic medium can be resolved. The numerical analysis of impedance functions of surface and embedded foundations on elastic soil placed on the fluid-filled poro-elastic half-space were done and the effect of elastic soil thickness and the embedded depth on impedance were investigated.
(4) Finally, works in this paper were summarized and suggestions on further research were given.
引文
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[2] Jones, J.P., Pulse Propagation in a Poroelastic Solid[J], J.Appl.Mech.,Vol.36, No.4,1969,pp879-880
[3] Halpern, M.R. et a1.Dynamic Impedence of a Porous Subgrade, Third ASCE-EMD Specialty Conf Univ of Texas, Austin, 1979
[4] Simon,B.R.,Zienkiewicz, O. C. and Paul,D.K.,An Analytical Solution for The Transient Response of Saturated Porous Elastic Solids[J],Int.J.Numer.Anal.Methods Geomech.Vol.8, 1984,pp381-398.
[5] Van Der Grinten, J.G.M. and Van Dongen,M.E.H.,Strain and Pore Pressure Propagation in a Water-Saturated Porous Medium[J],J.Appl.Phys.,Vol.62,1987,pp4682-4687.
[6] Gajo,A. and Mongiovi,L.,An Analytical Solution for The Transient Response of Saturated Linear E1astic Porous Media[J],Int.J.Numer.Anal. Methods Geomech.Vol.19,1995,pp399-413.
[7] Gajo,A.,Influence of Viscous Coupling in Propagation of glastic Waves in Saturated Soil[J],J.Geotech.Eng.,Vol.121,No.9,1995,pp636-644.
[8] Paul,S.,On the Displacements Produced in a Porous Elastic Half-Space by an lmpulsive Line Load(non-dissipative case),Pure.Appl.Geophys[J]., Vol.114,1976,pp605-614.
[9] Paul,S.,On the Disturbance Produced in a Semi-Infinite Poroelastic Medium by a Surface Lead,Pure.Appl.Geophys[J].,Vol.114,1976,pp6l5-627.
[10] Burridge,R. and Vargas, C.A.,The Fundamental Solution in Dynamic Poroelasticity. Geophys. J.R.Astr.Soc[J].,Vol.58,1979,pp8l-90.
[11] Norris,A.N.,Radiation From a Point Source and Scattering Theory in a Fluid-Saturated Porous Solid,J.Acoust.Sec.Am[J].Vol.77,1985, pp2012-2023.
[12] Chen,J.,Time Domain Fundamental Solution to Biot Complete Equations of Dynamic Poroelasticity, Part I:Two-Dimensional Solution, Int.J.Solids Structure[J],Vol.31,No.10,1994, ppl447-1490.
[13] Chen,J.,Time Domain Fundamental Solution to Biot Complete Equations of Dynamic Poroelasticity, PartⅡ:Three-Dimensional Solution,Int.J Solids Structure[J], Vol.31, No.10,1994, ppl69-202
[14] Philippacopoulos,A.J.,Waves in a Partially Saturated Layered Half-Space:Analytic Formulation,Bull.Seism.Soc.Am[J].,Vol.77,NO.5,1987, pp1838-1853.
[15]王立忠,陈云敏,吴世明等,饱和弹性半空间在低频谐和集中力下的积分形式解[J],水利学报,No.2,1996,pp84-88.
[16]杨峻,层状饱和土中波的传播[D],浙江大学博士学位论文,1996.
[17]杨峻,吴世明,陈云敏,弹性层饱和半空间体系稳态动力响应[J],土木工程学报, Vol.30,1997,pp39-47.
[18]丁伯阳,樊良本,吴建华,两相饱和介质中的集中力点源位移场解与应用[J],地球物理学报,Vol.42,No.6,1999,pp800-807.
[19]徐长节,蔡袁强,吴世明,饱和土中球空腔的瞬态动力响应[J],力学学报,Vol.32,No.4,2000,pp473-480.
[20]黄义,张玉红,饱和土三维非对称Lamb问题[J],中国科学(E辑),Vol.30,No.4,2000,pp375-384.
[21] Garg,S.K.,Wave Propagation Effects in a Fluid-Saturated Porous Solid, J.Geophys.Res. [J], Vol.76,NO.32,1971,pp7947—7962.
[22] Garg,S.K.,Nayfeh,A.H. and Good,A.J.,Compressional Waves in Fluid Saturated Elastic Porous Media,J.Appl.Phys[J].Vol.45,NO.5,1974,ppl968-1974.
[23] Garg,S.K.,Brownell,D.H.,Pritchett,J.W. and Herrmann,R.G., Shock-Wave Propagation in Fluid-Saturated Porous Media,J.Appl.Phys[J].Vol.46,NO.2, 1975,pp702-713.
[24] Chen,B.F. and Hung,T.,Dynamic Pressure of Water and Sediment On Rigid Dam[J],J.Eng. Mech., ASCE,Vol.119,No.7,1993, ppl411—1433.
[25]崔杰,砂土液化过程的动力分析[D],硕士学位论文,国家地震局工程力学研究所,1987.
[26] Ghaboussi,.J. and Wilson,E.L., Variational Formula of Dynamics of Fluid-Saturated Porous Elastic Solids[J],J.Eng.Mech.Div.,ASCE,EM4,1972,pp947-962.
[27] Ghaboussi,J.and Wilson, E.L., Seismic Analysis Of Earth Dam-Reservior Systems[J],J. Soil.Mech.Found.Div.,ASCE,Vol.99,SM10,1973,pp849—862.
[28] Ghaboussi,J.and Dikmen,S.U.,Liquefaction Analysis of Horizontally Layered Sands, J.Geotech. Div[J].,ASCE,GT3,1978,pp341-356.
[29] Simon,B.R.,WU,J.S. Zienkiewicz,O.C,and Paul,D.K.,Evaluation of u ? wand u ?πFinite Element Methods for the Dynamic Response Of Saturated Porous Media Using One-Dimensional ModelS,Int.,J,Numer.Anal.Methods Geomech[J]. Vol.10,NO.5,1986,pp461—482.
[30] Simon,B.R.,WU,J.S. and Zienkiewicz,O.C.,Evaluation of Higher Order, Mixed and Hermitean Finite Element Procedures for Dynamic Analysis of Saturated Porous Media Using One-Dimensional Models[J],Int.,I.Numer.Anal. Methods Geomech.Vol.10,NO.5,1986,pp483—499.
[31] Prevost,J. H.,Wave Propagation in Fluid-Saturated Porous Media:An Efficient Finite Element Procedure[J],Soil.Dyn.Earthq.Eng.,Vol.4,NO.4, 1985,ppl83-201.
[32] Sandhu,R.S.and Hong, S.J., Dynamics of Fluid-Saturated Soils variational formulation,Int.J Numer,.Anal.Methods Geomecht[J],Vol.11, 1987, pp241-255.
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