含定向非均匀体固体材料的横观各向同性有效弹性模量

Variation of effective elastic moduli of a solid with transverse isotropy due to aligned inhomogeneities

针对非均匀体定向指向的情况,将非均匀体对弹性波的散射等效为球形有效体对弹性波的散射,推导出了呈现横观各向同性的有效弹性模量.理论分析表明:本文得到的有效模量公式至少具有二阶精度.数值计算表明:本文的有效模量随孔隙度增加而降低,不会出现Hudson模型中在孔隙度超过一定阈值后不减反增的问题.另外,在非均匀体指向随机的情况,本文得到的有效模量公式归结为Kuster-Toks z模型的公式.对于由扁状裂隙作为非均匀体的孔隙岩石,裂隙内液体主要影响横观各向同性对称轴方向的纵波模量.

In this paper the efective or overall moduli of a solid containing aligned ellipsoidal inhomogeneties,are derived by making the scattered displacement feld equal to that scattered by a spherical–shaped efective medium in the same matrix.It is shown that the obtained formulae of efective elastic moduli are of second-order accuracy at least.The efective moduli decrease monotonically with porosity,thus excluding the unphysical behavior in Hudson＇s model in which there is an increase of moduli with porosity when the porosity goes beyond a certain threshold.By integration of inhomegeneity orientation angle,the efective moduli can be obtained for a solid with randomly orientated inhomogeneities,which are the same as those in the Kuster-Toks z model.Numerical calculations show that a rock with fuid-saturated inhomegeneities has a higher longitudinal wave modulus in the direction of TI symmetric axis than the modulus for a rock with empty inhomegeneities.