埋置力源下横观各向同性饱和地基的三维Lamb问题解答

3D Lamb’s problm in transversely isotropic saturated soils subjected to internal excitation

基于横观各向同性饱和介质的三维Biot波动方程,首先引入位移函数,将圆柱坐标系下的波动方程解耦,并利用算子理论,给出了Biot波动方程的通解。利用Fourier展开和Hankel变换,求解波动方程,得到土骨架位移、孔隙水压力和饱和介质总应力分量的积分形式一般解。其次,系统研究了横观各向同性饱和半空间体在埋置动力荷载作用下的三维Lamb问题,结合边界条件,给出了问题的基本解。算例表明,水平力作用下,荷载埋置较浅时,地表竖向位移幅值沿径向衰减迅速,埋深和频率增大时,地表位移波动性增强,衰减不明显。

Based on the Biot＇s theory for fluid-saturated porous media, the 3D wave equations for transversely isotropic saturated soils in cylindrical coordinate are transformed into the two uncoupling goveming differential equations by introducing displacement functions, and the general solutions are presented by the operator theory. Then, the differential equations are solved by the Fourier expanding and Hankel integral transform methods. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for saturated soils are obtained. Furthermore, the systematic study on Lamb＇s problems in the transversely isotropic saturated soils subjected to the internal excitation is performed. The calculated results indicate the rapid vibration attenuation of vertical surface displacement of the saturated soils subjected to a low-frequency interior excitation in small depth.