Three-Dimensional Frequency-Domain Green’s Functions of a Finite Fluid-Saturated Soil Layer Underlain by Rigid Bedrock to Interior Loadings
Shiping Zhang, Ronald Y. S. Pak, Junhui Zhang
Abstract
This paper presents the three-dimensional frequency-domain Green’s functions of a saturated poroelastic soil layer with incompressible constituents resting on rigid base due to interior time-harmonic point-, ring-, and disc-loadings with uniform distribution being composed of three effective stress source components and one pore fluid pressure source. The set of Green’s functions can provide complete fundamental solutions for relevant boundary-value problem studies by the method of boundary integral equations. In developing these solutions, the dynamic property of the porous medium is described by Boer’s poroelastic model. Four independent wave equations with definite physical meaning are obtained by introducing four scalar displacement potentials to uncouple the equations of motion of the layer and then resolved by the Fourier–Hankel integral transformations. By imposing the boundary and load interfacial conditions of the layer, the Green’s function solutions of all field variables corresponding to the point-, ring-, and disc-loadings are derived. The obtained solutions are then validated by comparing with the existing special solutions and the finite-element model (FEM) calculation results. Numerical examples with disc loading cases are also performed to examine the effects of the permeability and the thickness of the poroelastic layer on its dynamic characteristic.