%0 Journal Article
%T Analysis of Transient Dynamic Behaviour of Spherical Cavity in Viscoelastic Soil Medium
%A J. P. Dwivedi
%A V. P. Singh
%A Radha Krishna Lal
%J ISRN Mechanical Engineering
%D 2013
%R 10.1155/2013/186204
%X Stress, displacement, and pore pressure of a partially sealed spherical cavity in viscoelastic soil condition have been obtained in Laplace transform domain. Solutions of axisymmetric surface load and fluid pressure are derived. 1. Introduction Biot [1, 2] presented the propagation theory of elastic waves and the general solutions for fluid-saturated porous viscoelastic medium. Akkas and Zakout [3] discussed the solution for the transient response for an axisymmetric and nontorsional load of an infinite, isotropic, elastic medium containing a spherical cavity with and without thin elastic shell embedment. In this paper, considering a viscoelastic model presented by Eringen [4], the transient response of a spherical cavity with a partially sealed shell embedded in viscoelastic soil is investigated. The solutions of stresses, displacements and pore pressure induced by axisymmetric surface load and fluid pressure are derived in Laplace transform domain. Durbin¡¯s [5] inverse Laplace transform is used to analyze the influence of partial permeable property of boundary and relative rigidity of shell and soil on the transient response of the spherical cavity. The solutions of permeable and impermeable boundary without shell are considered as two extreme cases. 2. Basic Equations and Solutions In infinite viscoelastic saturated soil, a thin elastic shell shown in Figure 1 with inner radius , outer radius , and thickness , has been bored. are the spherical coordinates, where and are the meridional and circumferential angles, respectively, , , are nonvanishing components of stress tensor in case of an axisymmetric nontorsional load, that is, independent of and acting on the shell surface. Figure 1: Geometry of the problem. In spherical coordinate system , the equilibrium equation for soil mass is where and are radial displacement of soil skelton and displacement of pore fluid with respect to soil skelton, respectively; , the density of soil; and are densities of fluid and soil grains respectively; is porosity. The pore fluid equilibrium equation is given by where is excess pore pressure; is the fluid viscosity, and is the intrinsic permeability of soil. Soil is not an ideal medium. Due to overcoming the interior friction of soil, a part of energy of the propagation wave is changed into heat energy during the propagation. This property is known as damping of material. Assuming that the viscoelastic property of soil may be simulated by Kelvin-Voigt model. Following Eringen [4], the stress-strain relationship is expressed as where and , dilations of solid and fluid,
%U http://www.hindawi.com/journals/isrn.mechanical.engineering/2013/186204/