流体饱和多孔介质中波传播问题的有限元分析

Finite Element Analysis of Wave Propagation in Fluid-Saturated Porous Media

1.
Department of Engineering Mechanics, Chongqing University, Chongqing 400044, P R China;
2.
Shantou University, Shantou 515063, P R China

摘要: 采用基于混合物理论的多孔介质模型,给出流体饱和两相多孔介质波动问题的有限元分析方法。采用罚方法导出的有限元动力方程,时间积分可采用显式和隐式积分两种方案。用编制的有限元程序分析了一维柱体在跃阶载荷和脉冲载荷作用下的波传播问题,得到该两种瞬态载荷作用下固体和流体相位移、速度以及固体相有效应力和孔隙压力随时间的变化关系,并对波的传播现象进行了分析。所得结果与理论相吻合。
- 多孔介质 /
- 波的传播 /
- 有限元
Abstract: With the porous media model based on mixture theory,a finite element formulation for dynamic transient analysis of fluid-saturated two-phase porous media is presented.Time integration of the equation,deduced with penalty method,can be performed by using implicit or explicit method. One-dimensional wave propagation in column under step loading and impulsive loading are analyzed with the developed finite element program.The obtained curves of displacements,velocities,effective stresses and pore pressures against time demonstrate the existence of wave propagation phenomena,which coincide with the theoretical results.
- porous media /
- wave propagation /
- finite element method

[1]	Biot A M. The theory of propagation of elastic wave in a fluid-saturated porous solid, Ⅰ Low-frequency range; Ⅱ Higher-frequency range[J]. J Acoust Soc Amer,1956,28(2):168～178,179～191.
[2]	Zienkiewicz O C. Shiomi T. Dynamic behavior of saturated porous media: the generalized Biot formulation and its numerical solution[J]. Internat J Numer Anal Methods Geomech,1984,8(1):71～96.
[3]	Simon B R, Wu S S, Zienkiewicz O C, et al. Evaluation of u-w and u-π finite element method for dynamic response of saturated porous media using one-dimensional model[J]. Internat J Numer Anal Methods Geomech,1986,10:461～482.
[4]	de Boer R. 多孔介质理论发展史上的重要成果[M]. 刘占芳,严波(译). 重庆: 重庆大学出版社,1995.
[5]	Bowen R M. Incompressible porous media by use of the theory of mixtures[J]. Internat J Engrg Sci,1980,18(1):19～45.
[6]	Bowen R M. Compressible porous media by use of the theory of mixtures[J]. Internat J Engrg Sci,1982,20(6):697～735.
[7]	de Boer R, Ehlers R, Liu Z. One-dimensional transient wave propagation in fluid-saturated incompressible porous media[J]. Arch Appl Mech,1993,63:59～72.
[8]	Zienkiewicz O C, Taylor R L. The Finite Element Method[M]. Vol 1.4th edn. London: McGraw-Hill,1989.
[9]	Hughes T J R, Pister K S, Taylor R L. Implicit-explicit finite elements in nonlinear transient analysis[J]. Comput Methods Appl Mech Engrg,1979,17/18:159～182.