饱和土埋置力源的三维动力Lamb问题解答

基于一组弹性土波动方程，应用Fourier级数展开和Hankel积分变换，得到了三维问题饱和土骨架与孔隙水的应力及位移分量在变换域内的积分形式通解．考虑地基表面透水情形，由边界条件导出了半空间饱和土体在埋置力源作用下的三维动力Lamb问题的解答．给出了埋置水平力作用下地基表面竖向位移、径向位移及周向位移的数值解．该研究为运用边界元法求解饱和地基的动力响应课题奠定了理论基础．

THREE-DIMENSIONAL LAMB'S PROBLEM OF SATURATED SOILS SUBJECTED TO INTERNAL EXCITATION

Based on a modified theory of elastic wave in saturated soils, general solutions for the displacements and stress components of the saturated soils are obtained by using Fourier series expansion and Hankel transform. Under the consideration of boundary-value condition, these solutions are used to solve the three dimensional Lamb's problem of saturated soils corresponding to arbitrary loads applied at a finite depth below the surface. Particularly, the displacement components in vertical, radial and azimuthal directions at the surface of saturated soils subjected to horizontal internal excitation are presented numerically. Green's functions presented can be used to solve a variety of dynamic boundary-value problems for saturated soils as the fundamental functions in the boundary integral method.