3-D Non-axial Symmetrical Lamb Problem Of Layered Saturated Half-Space With Base Rock

The steady dynamical response of the saturated half-space activated by a non-axial symmetrical concentrated harmonious load on the surface is a very important theme in the theory of half-space foundation vibration. The theme is valuable in theory and application. The saturated soil is considered a fluid-saturated porous solid and it is appropriate to be studied by the theory of two kinds of media. In practice, the foundation is layered saturated half-space. Also there is rock under the saturated soil which is named of layered saturated space with base rock.The paper first illation the Lamb problem and the basic theory and idea are introduced into this paper. The paper is based on general theory of 3-D consolidation 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 low frequency in the paper. In addition, the paper assumes that the media can't be compressed and the inertia of the fluid can be ignored. According to above assumption, the Hankel transformations of displacement and stress are applied and the solutions for saturated space problem are obtained. Radiation conditions of wave are applied and the solutions for half-saturated space problem are obtained. Saturated soil is reduced to elastic soil and the solutions for elastic space problem are obtained. Apply to boundary conditions of displacement and stress between the two soil layers, the boundary conditions of the surface stress, the solutions for elastic space problem and saturated space problem and saturated half-space problem, the integral solutions for the non-axial symmetrical Lamb's problem of saturated half-space based on an elastic soil layer and an saturated soil layer and layered saturated space with base rock are obtained. The non-axial symmetrical Lamb's problem is inferred by the two different boundary conditions when it is undrained.The paper reduces the Lamb problem of the layered saturated half-space to the Lamb problem of the saturated half-space and the Lamb problem of the elastic half-space and the reduced integral solutions are same to the present thesis. Numerical calculation is applied in the paper through accelerated integral means. The study is useful to engineering practice.