三维横观各向同性层状地基任意点格林函数求解

Solution to Green's functions for arbitray points in 3D cross-anisotropic multi-layered soil

提出了求解横观各向同性层状地基表面或内部任意点位移格林函数的混合数值算法。此算法利用Fourier变换将频率–空间域的波动方程转换到频率–波数域内的状态方程,采用高精度的精细积分算法进行求解,得到频率–波数域内的动力柔度矩阵,最后利用Fourier逆变换得到频率–空间域内任意点的位移格林函数。提出的算法适用于任意横观各向同性层状地基,对地基层数和单层的厚度均没有任何的限制。数值算例验证了算法的准确性,并针对层状地基的各向异性特性进行了参数分析。

A hybrid numerical method is proposed to evaluate the Green＇s functions for displacement of surface or internal arbitrary points in cross-anisotropic multi-layered soil. The wave motion equations in fxequency-spatial domain are transformed into state equations in frequency-wavenumber domain using the Fourier transform. Then the dynamic flexibility matrix is obtained. Finally, the inverse Fourier transform is used to evaluate the Green＇s fimctions for displacement of arbitary points in i^equency-spatial domain. The proposed algorithm is suitable for arbitrary cross-anisotropic multi-layered soil, and there are no limitations for the number and thickness of the layers. The accuracy of the proposed method is validated by numerical examples, and a parameter analysis for the anisotropy of multi-layered soil is presented.