Fundamental solution for the time-harmonic vertical vibration of a rigid circular disc embedded in a transversely isotropic and layered poroelastic half-space is developed using a semi-analytical method. First, based on the Green's function of the time-harmonic vertical circular load embedded in the layered half-space, function of the corresponding annular ring load is determined via the method of superposition. Then the disc-medium contact area is discretized into annular ring elements with unknown densities which are determined via an integral least-square approach. Finally, the dynamic vertical compliance is derived by virtue of the equilibrium between the applied load on the disc and the resultant contact stress. Based on the derived fundamental solution, selected numerical examples on the dynamic vertical compliance are presented to investigate the influence of the surface hydraulic condition, fluid saturation, embedment depth of the disc, material anisotropy, material layering, and input frequency.

利用半解析方法，研究了嵌入在横向各向同性和分层多孔弹性半空间中的刚性圆盘的时谐垂直振动的基本解决方案。首先，基于叠加在分层半空间中的时谐垂直圆形载荷的格林函数，通过叠加法确定相应的环形载荷的函数。然后，将圆盘介质的接触区域离散为密度未知的环形环，该环形环通过整数最小二乘法确定。最后，借助于在盘上施加的载荷与所产生的接触应力之间的平衡来得出动态垂直顺应性。根据导出的基本解决方案，