横观各向同性饱和地基三维瞬态Lamb问题

研究了横观各向同性饱和土地基在地表动力荷载作用下的三维瞬态响应。基于饱和多孔介质的三维Biot波动理论，利用Laplace变换，建立圆柱坐标系下横观各向同性饱和土的波动方程；解耦波动方程后，根据算子理论，并借助Fourier展开和Hankel变换技术，得到瞬态荷载作用下，饱和土介质的土骨架位移和应力、孔隙水相对位移和孔隙水压力的一般解；利用一般解，给出横观各向同性饱和地基在地表集中荷载激励下的瞬态Lamb问题的解答。数值算例结果表明，采用各向同性饱和介质的动力学模型，不能准确描述具有明显各向异性特性的饱和土地基的瞬态动力特性。

Three-dimensional transient Lamb's problem of transversely isotropic saturated soils

The three-dimensional (3D) transient dynamic response of transversely isotropic saturated soils due to surface loads is studied. First, based on Biot’s 3D wave theory for fluid-saturated porous media, the governing differential equations in cylindrical coordinate are presented by Laplace transform. Then, according to operator theory, the general solutions of soil skeleton and fluid displacements and pore pressure as well as the total stresses for saturated soils are presented by means of Fourier expanding and Hankel integral transform. Furthermore, using general solutions, the transient solutions for Lamb’ problem of transversely isotropic saturated half-space to impulsive concentrated loading are presented. Numerical results show the obvious difference between the model of isotropic saturated poroelastic media and that of transversely isotropic saturated poroelastic media.