Three-Dimensional Non-axisymmetric Lamb Problem Of Layered Saturated Half-Space

The steady dynamical response of the saturated half-space activated by anon-axisymmetric concentrated harmonious load on the surface is a very important themein the theory of half-space foundation vibration. The theme is valuable in theory andapplication. The saturated soil is considered a fluid-saturated porous solid and it isappropriate to be studied by the theory of two kinds of media. In practice, the foundationis composed of soil layers, which is named layered saturated half-space.The paper first illation the Lamb problem and the basic theory and idea areintroduced into this paper. The paper is based on general theory of three-dimensionalconsolidation and theory of propagation of elastic waves in a fluid-saturated porous solid,which are delivered by Biot. The frequency of harmonious load is limited to lowfrequency in the paper. In addition, the paper assumes that the media can't be compressedand the inertia of the fluid can be ignored. According to above assumption, the Hankeltransformations of displacement and stress are applied and the solutions for saturatedspace problem are obtained. Radiation conditions of wave are applied and the solutionsfor half-saturated space problem are obtained. Saturated soil is reduced to elastic soil andthe solutions for elastic space problem are obtained. Apply to boundary conditions ofdisplacement and stress between the two soil layers, the boundary conditions of thesurface stress, the solutions for elastic space problem and saturated space problem andsaturated half-space problem, the integral solutions for the non-axial symmetry Lamb'sproblem of saturated half-space based on an elastic soil layer or an saturated soil layer areobtained, that is to say, the integral solutions for three-dimensional non-axisymmetricLamb problem of layered saturated half-space.The paper reduces the Lamb problem of the partial saturated half-space to the Lambproblem of the saturated half-space and the Lamb problem of the elastic half-space andthe reduced integral solutions are same to the present thesis, which proves that theintegral solutions for the non-axisymmetric Lamb's problem of the partial saturatedhalf-space are accurate. Numerical calculation is applied in the paper through acceleratedintegral means and the results are the same to the present thesis. The study is useful toengineering practice.