Dynamic Response Of A Pile Embedded In A Saturated Soil To Elastic Waves

Based on the integral equation method, the response of a pile embedded in a saturated soil half-space subjected to elastic waves is investigated in this paper. The studies of the paper consist of the following parts:1. The fundamental solutions for a saturated half-space subjected to a circular patch load. The fundamental solutions of this paper, which correspond to the solutions for a circular patch load applied within a half space saturated soil, consist of displacement, stress, strain and pore pressure. The governing equations for Biot's theory are reduced to Helmholtz equations for two scalar potentials and a vector potential. The potentials can be further expanded into the Fourier series. The general solutions for the potentials can be obtained by using the Hankel tansform method. The expressions for the fundamental solution in transformed domain can be obtained by using of the general solution for the potentials, boundary conditions of the free surface and the continuity conditions at the plane of the patch load. The fundamental solution in the frequency domain can be obtained by numerical inversion of the Hankel tansform.2. The elastic wave field solution. Based on Biot's theory and the Fourier transform method, the Helmholtz equations for the potentials of the saturated soil are derived. The wave field solutin for the Rayleigh wave and the P or SV wave can be determined by the boundary conditions of the half space and the general solutions for the potentials. The attenuation for the two Rayleigh waves, the displacement and the pore pressure, the pore pressure and the displacement of the P or SV wave field are discussed.3. Dynamic response of a single pile embedded in a saturated soil. Based on the fictitious pile methodology, the original pile soil interaction problem is reduced to the superposition of an extended soil half space and a fictitious pile. The extended soil half space is described by Biot's theory, while the fictitious pile is treated by the bar and beam vibration theory. The second kind of Fredholm integral equation for the pile is established by using the fundamental solution, the elastic wave field and the pile-soil compatibility conditions. Solution of the integral equation yields the dynamic response of the pile-soil system. Numerical results demonstrate that the permeability, the porosity of the soil, modulus ratio berween pile and soil, Poisson's ratio, the frequency of the incident wave have significant influences on the dynamic response of the soil-pile system.