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利用波函数展开法给出了入射平面P波在饱和半空间中圆形洞室周围散射问题的一个解析解。半空间假定为无粘性流体饱和介质,满足Biot理论。采用一种基于实验数据的孔隙率和模量之间的线性关系来确定Biot模型中的介质参数。解答考虑了透水边界和非透水边界两种情况。对边界条件进行了数值检验,结果表明,随着级数截断项数的增大,边界残量衰减很快。解答为进一步研究入射波频率和角度、边界渗透条件、孔隙率、泊松比等参数对散射的影响奠定了基础。
An analytic solution to the scattering problem of the P wave in the plane of a circular cavity in a saturated half space is given by using the wave function expansion method. The half-space is assumed to be a viscous fluid-saturated medium that satisfies Biot's theory. A linear relationship between porosity and modulus based on experimental data was used to determine the media parameters in the Biot model. The solution considers both the pervious and non-pervious boundaries. The boundary conditions were tested numerically. The results show that the residuals of the boundary decay rapidly with the increase of the number of series truncation. The solution laid the foundation for the further study on the effects of incident wave frequency and angle, boundary infiltration conditions, porosity and Poisson's ratio on the scattering.