流体饱和半空间中埋置球面P1、P2和SV波源动力格林函数

基于Biot流体饱和孔隙介质理论,采用Hankel积分变换方法,在频域内求解了流体饱和半空间中埋置球面P1、P2和SV波源的动力格林函数。首先由Hankel积分变换将空间域内球面波展开为波数域内柱面波的叠加;然后在半空间表面对称位置虚拟放置一同样大小的球面波源,这样对于球面膨胀波源(P1和P2波源),地表剪应力为零,但存在非零正应力和孔隙水压,对于球面剪切波源(SV波源),地表正应力和孔隙水压为零,但存在非零剪应力;最后叠加球面波源、虚拟波源和残余半空间表面应力产生的动力响应,即可求得流体饱和半空间中埋置球面波源波数域内的动力响应,空间域内埋置球面波源的动力格林影响函数则由Hankel逆变换求得。该文给出的球面波源动力格林函数,为建立以球面P1、P2和SV波动力格林函数为基本解的间接边界元方法,求解饱和多孔介质中三维轴对称弹性波散射问题奠定了基础。

Dynamic Green's functions of spherical P1, P2 and SV sources embedded in a water-saturated half-space

The dynamic Green's functions of spherical dilatational source P1, P2 and SV-waves embedded in a water saturated half-space in the frequency domain are presented based on Biot's theory. Firstly, the spherical source in the space domain is expressed as the summation of cylindrical waves in the wave number domain using the Hankel transformation, and the image of the spherical source is introduced. For the dilatational source, the shear stress becomes zero with non-zero normal stress and pore pressure at the surface of the half-space, which are defined as the residual normal stress and pore pressure;while for the shear source, the normal stress and pore pressure become zero with none-zero shear stress, which is defined as the residual shear stress. Finally, the total responses in the wave number domain are obtained by adding the responses of the reversed residual stress, the residual pore pressure, the spherical source and the virtual spherical source, while the Green's functions in the space domain can be obtained by inverse Hankel transformation. The dynamic Green's functions presented in this paper can be used as the fundamental solutions for the indirect boundary element method, which is expected to contribute to solve symmetric three dimensional wave scattering problems in water saturated half-space.