饱和土半空间中圆柱形孔洞对平面P波的散射

在 Biot饱和多孔介质动力学理论的基础上，首次建立了求解饱和土半空间中圆柱形孔洞对平面 P 波散射问题的波函数展开法。首先。分析了具有圆柱形孔洞的饱和土半空间场地在平面 P 波入射下产生散射波系，并将入射波和散射波的波函数在圆柱坐标下展开。然后，引入边界条件，求出散射波函数的待定系数，从而，得到饱和土半空间中圆柱形孔洞对平面P波的散射问题的解析解。根据所得的波函数的解，可求解区域内的位移、应力的值，同时，分析了入射波频率、入射角对柱面上的应力集中因子的影响。

An analytical solution for diffraction of plane P-waves by cylindrical cavity in a fluid-saturated porous media semi-space

On the basis of Biot dynamic theory, the dynamic response of cylindrical cavities to incident P waves is investigated. An analytic solution is derived for a cavity embedded within a fluid-saturated porous media semi-space for the first time in this paper. The waves scattered by the cavity and semt-space are expressed in the term of wave potentials and expended in Fourier-Bessel series, and the coefficients in the wave functions are determined to satisfy the boundary conditions. By using the solutions of the potentials, the expressions of the displacements and stresses can be obtained. Numerical results are given and the dynamical stress concentration factor on the surface of the cavity that are presented shows that the results depend on the angle of incidence, the dimensionless frequency of the incident P wave.