横观各向同性饱和无限土体三维粘弹性动力时域解

3-D viscoelastic dynamic analysis of transversely isotropic saturated poroelastic soil in time domain

根据横观各向同性饱和土体的三维动力方程,运用Fourier展开、Laplace和Hankel变换方法,求解了横观各向同性饱和土体的粘弹性动力反应问题。给出了土骨架位移分量、孔隙流体相对于土骨架的位移分量和孔隙流体压力的积分形式一般解。并对横观各向同性饱和土体动力响应边值问题的求解过程作了系统说明。为了求得时域内的数值解,利用Laplace Hanke数值逆变换编制了计算程序,研究了对垂直向和水平向圆形动力荷载作用下半空间边值问题。

Based on the 3-D dynamic equations for transversely isotropic saturated poroelastic media the Fourier expansion approach, and Laplace-Hankel transformation are used to solve the viscoelastic dynamic response of the transversely isotropic saturated soil. The general solutions are derived in terms of solid matrix displacements and fluid displacement relative to the soil matrix. The process for calculating dynamic response in poro-viscoelastic half-space is given. The solutions in time domain can be obtained by using numerical inverse Laplace-Henkel transforms, and the computational program is developed. The boundary-value problems of transverse isotropic saturated poro-viscoelastic half-space under the action of vertical and horizontal dynamic loads are solved when initial condition and boundary condition are given. The numerical results for solid matrix displacement and pore pressure are presented. The comparison shows that the proposed solution possesses enough accuracy.