| 饱和多孔微极介质的波动方程及其势函数方程 |
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| 引用本文： | 胡亚元.饱和多孔微极介质的波动方程及其势函数方程[J].地球物理学报,2005,48(5):1132-1140. |
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| 作者姓名： | 胡亚元 |
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| 作者单位： | 浙江大学岩土工程研究所，杭州 310027 |
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| 基金项目： | 浙江省留学归国基金资助(J20050026). |
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| 摘 要： | 土是由一定尺寸大小颗粒所构成的多孔介质，具有明显的颗粒特性，当土颗粒间的孔隙被流体（如水或油）充满时则成为饱和土.利用微极理论和Biot波动理论的研究成果，把饱和土中多孔固体骨架部分近似地视为微极介质，孔隙中的流体部分视为质点介质，获得饱和多孔微极介质的弹性波动方程.借鉴Greetsma理论，建立了饱和多孔微极介质弹性本构方程力学参数与相应单相介质弹性参数的相互关系，使饱和多孔微极介质弹性波动方程中的物理参数具有明确的物理意义，易于在试验中确定.运用场论理论把饱和多孔微极介质的波动方程简化为势函数方程，建立了饱和多孔微极介质中五种弹性波的弥散方程，数值分析了五种简谐体波在无限饱和多孔微极介质中的传播特性. 结果表明，P1波、P2波和剪切S1波的波速弥散曲线与经典饱和多孔介质基本相同，当频率小于临界频率ω0时旋转纵波θ波和横波S2波不存在，当频率大于临界频率ω0时，θ波和S2波的传播速度随频率增加而减小.
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| 关 键 词： | 土动力学 多孔微极介质 Biot波动方程 势函数方程 简谐波 传播特性 |
| 文章编号： | 0001-5733（2005）05-1132-09 |
| 收稿时间： | 2004-08-23 |
| 修稿时间： | 2004-08-232005-05-10 |
Pragmatic wave equations and their potential equations of a saturated porous micropolar medium |
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| HU Ya-yuan.Pragmatic wave equations and their potential equations of a saturated porous micropolar medium[J].Chinese Journal of Geophysics,2005,48(5):1132-1140. |
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| Authors: | HU Ya-yuan |
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| Institution: | Institute of Geotechnical Engineering, Zhejiang University, Hangzhou 310027, China |
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| Abstract: | Soil is a porous medium made of rigid grains in the microscale and has an obvious grain behavior. It becomes a saturated soil when pores between soil grains are filled with water or oil. When the porous solid skeleton is approximately taken as a micropolar medium and the fluid in the pores a point medium, the elastic pragmatic wave equations in a saturated porous micropolar medium are obtained from the results of the micropolar theory and those of Biot's pragmatic wave theory. The relations between the parameters of the saturated porous micropolar theory and those of the corresponding one_phase medium are established by means of the Greetsma theory. It has merits that the physics parameters in our dynamic equations of the saturated porous micropolar medium have a definite physics meaning and are easy to be tested in laboratory. The dynamical equations are then simplified as the potential equations with the aid of the field theory and the dispersion equations of five elastic waves propagating in the saturated porous micropolar medium are established. Finally, the propagating characteristics of the five harmonic body waves in the saturated micropolar porous medium are investigated by numerical methods. The result showns that the dispersion curves of the velocities of P1 wave, P2 wave and shear S1 wave are similar to those in the classical saturated porous medium. When frequency is lower than the critical frequency ω0，either the rotation longitude θ wave or the rotation transverse S2 wave does not exist. When the frequency is greater than the critical frequency ω0，θ wave and S2 wave both arise and their velocities decrease with increasing frequency. |
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| Keywords: | Soil dynamics Porous micropolar medium Biot's wave equation Potential equations Harmonic waves The pragmatic characteristics |
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