基于Biot理论多种简化模型的适用性研究
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摘要
基于Biot理论提出的简化模型主要包括以下简化形式:忽略混合物动力平衡方程和广义达西定律中相对加速度项;忽略混合物动力平衡方程中相对加速度项以及广义达西定律中所有惯性项;忽略控制方程中所有惯性项。分析了多种简化模型在不同材料参数和不同激励频率作用下的适用性,基于不同简化模型得到了一维有限饱和土柱的位移和孔压的频域解析解,引入无量纲量综合考虑渗透系数、孔隙率和激励频率等参数的影响,并依据这些无量纲量分析各种简化模型的适用范围。
Based on the Biot's theory, three simplified formulations are proposed. The simplifications mainly include neglecting the relative acceleration terms in the dynamic mixture equilibrium equation and the generalized Darcy's law, neglecting the relative acceleration terms in the dynamic mixture equilibrium equation and all the inertial terms in the generalized Darcy's law,and neglecting all the inertial terms in the equations. The applicability of the simplifications are discussed with the help of analytical solutions for one-dimensional finite fully saturated poroelastic column. Two non-dimensional parameters are introduced to discuss the effects of permeability, excitation frequency and porosity.
Based on the Biot's theory, three simplified formulations are proposed. The simplifications mainly include neglecting the relative acceleration terms in the dynamic mixture equilibrium equation and the generalized Darcy's law, neglecting the relative acceleration terms in the dynamic mixture equilibrium equation and all the inertial terms in the generalized Darcy's law,and neglecting all the inertial terms in the equations. The applicability of the simplifications are discussed with the help of analytical solutions for one-dimensional finite fully saturated poroelastic column. Two non-dimensional parameters are introduced to discuss the effects of permeability, excitation frequency and porosity.
引文
[1]BIOT M A.General theory of three-dimensional consolidation[J].Journal of Applied Physics,1941,12(2):155-164.
[2]BIOT M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:Ⅱhigher frequency range[J].Journal of the Acoustical Society of America,1956,28(2):179-191.
[3]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 America,1956,28(2):168-179.
[4]BIOT M A.Theory of deformation of a porous viscoelastic anisotropic solid[J].Journal of Applied Physics,1956,27(5):459-467.
[5]ZIENKIEWICZ O C,CHANG C T,BETTESS P.Drained,undrained,consolidating and dynamic behaviour assumptions in soils[J].Géotechnique,1980,30(4):385-395.
[6]SCHANZ M,CHENG H D.Transient wave propagation in a one-dimensional poroelastic column[J].Acta Mechanica.2000,145(1/2/3/4):1-18.
[7]SCHANZ M,STRUCKMEIER V.Wave propagation in a simplified modelled poroelastic continuum:fundamental solutions and a time domain boundary element formulation[J].International Journal for Numerical Methods in Engineering,2005,64(13):1816-1839.
[8]ZIENKIEWICZ O C,SHIOMI T.Dynamic behaviour of saturated porous media:the generalized Biot formulation and its numerical solution[J].International Journal for Numerical&Analytical Methods in Geomechanics,1984,8(1):71-96.
[2]BIOT M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:Ⅱhigher frequency range[J].Journal of the Acoustical Society of America,1956,28(2):179-191.
[3]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 America,1956,28(2):168-179.
[4]BIOT M A.Theory of deformation of a porous viscoelastic anisotropic solid[J].Journal of Applied Physics,1956,27(5):459-467.
[5]ZIENKIEWICZ O C,CHANG C T,BETTESS P.Drained,undrained,consolidating and dynamic behaviour assumptions in soils[J].Géotechnique,1980,30(4):385-395.
[6]SCHANZ M,CHENG H D.Transient wave propagation in a one-dimensional poroelastic column[J].Acta Mechanica.2000,145(1/2/3/4):1-18.
[7]SCHANZ M,STRUCKMEIER V.Wave propagation in a simplified modelled poroelastic continuum:fundamental solutions and a time domain boundary element formulation[J].International Journal for Numerical Methods in Engineering,2005,64(13):1816-1839.
[8]ZIENKIEWICZ O C,SHIOMI T.Dynamic behaviour of saturated porous media:the generalized Biot formulation and its numerical solution[J].International Journal for Numerical&Analytical Methods in Geomechanics,1984,8(1):71-96.