Chapter 4 - Dynamic Responses of Foundations Under Elastic Waves

Abstract

Based on Biot's poroelastic theory, an investigation into the dynamic response of a rigid circular foundation on poroelastic soil excited by incident fast P waves, SV waves, and Rayleigh waves is described in this chapter. The incident and reflected wave fields are obtained by introducing potential functions. The radiation field and rigid-body scattering field are introduced in order to consider the dynamic interaction between the foundation and the underlying soil, as well as the scattering phenomena caused by the existence of the foundation. The motion of the soil is supposed to be governed by Biot's dynamic poroelastic theory, while the boundary conditions along the contact surface between the soil and bottom of the foundation are assumed to be perfectly bonded for the skeleton and hydraulically drained for the fluid. Combining with the mixed boundary-value condition and the dynamic equilibrium equation of the foundation, the expression of the vertical and rocking dynamic amplitude of the foundation subjected to the incident waves is obtained by solving the control equations using Hankel transforms. The influences of incident angle, the mass of the foundation and the permeability of the soil on the vertical vibrations of the foundation are thus determined through numerical calculations.