饱和多孔介质一维瞬态波动问题的解析分析
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摘要
采用基于混合物理论的多孔介质模型,提出了饱和多孔介质一维动力响应的初边值问题。利用拉氏变换和卷积定理,分别得到了边界自由排水时在任意应力边界条件和任意位移边界条件下瞬态波动过程的解析表达。几种典型的数值算例同时给出了两类边界条件下瞬态波动过程中多孔固体的位移场、应力场和孔隙流体的速度场、压力场。结果表明,饱和多孔介质的波动过程是多孔固体和孔隙流体中以同一速度传播的两种波动的耦合过程,时效特性分析也揭示了饱和多孔介质固有的表观粘弹性性质。
In the framework of porous media model developed from mixtures theories,an initial and boundary value problem is presented for one-dimensional dynamic response of porous media.Analytical solutions are obtained using Laplace transform and convolution theorem for the transient wave motion in saturated porous media under arbitrary stress boundary condition and displacement boundary condition,respectively.Through several illustrative numerical examples,the displacement and stress fields of solid skeleton as well as the velocity and pore pressure fields of interstitial fluid in transient wave motion under the two types of boundary conditions are discussed.It is demonstrated that the wave motion in saturated porous media is a coupled process of the waves in the skeleton and the interstitial fluid.The apparent visco-elasticity of saturated porous media is also discussed.
In the framework of porous media model developed from mixtures theories,an initial and boundary value problem is presented for one-dimensional dynamic response of porous media.Analytical solutions are obtained using Laplace transform and convolution theorem for the transient wave motion in saturated porous media under arbitrary stress boundary condition and displacement boundary condition,respectively.Through several illustrative numerical examples,the displacement and stress fields of solid skeleton as well as the velocity and pore pressure fields of interstitial fluid in transient wave motion under the two types of boundary conditions are discussed.It is demonstrated that the wave motion in saturated porous media is a coupled process of the waves in the skeleton and the interstitial fluid.The apparent visco-elasticity of saturated porous media is also discussed.
引文
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[3]Bowen R M.Incompressible porous media by use of the theory of mixtures[J].International Journal of Engineering Science,1980,18:19～45.
[4]Bowen R M.Compressible porous media by use of the theory of mixtures[J].International Journal of Engineering Science,1982,20:19～45.
[5]陈少林,廖振鹏.两相介质动力学问题的研究进展[J].地震工程与工程振动,2002,22(2):1～8.Chen Shaolin,Liao Zhenpeng.Advances in research on two-phase media dynamic problem[J].Earthquake Engineering and Engineering Vibration,2002,22(2):1～8.(in Chinese)
[6]Prevost H.Wave propagation in fluid-saturated porous media:an efficient finite element procedure[J].Soil Dynamics and Earth Engng,1985,4:183～202
[7]Lai W M,Mow V C,Zhu W.Constitutive modeling of articular cartilage and biomacromolecular solutions[J].Journal of Biomechanical Engineering,1993,115:474～480
[8]Liu Zhanfang.Wave propagation in an incompressible fluid-saturated porous medium[D].Chongqing:Chongqing University,1992.
[9]R de Boer,Ehlers W,Liu Z.One-dimensional transient wave propagation in fluid-saturated incompressible porous media[J].Archive of Applied Mechanics,1993,63(1):59～72
[10]杨大地,涂光裕.数值分析[M].重庆:重庆大学出版社,1998.Yang Dadi,Tu Guangyu.Numerical analysis[M],Chongqing:Chongqing University Press,1998.(in Chinese)
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