Dynamic Analysis of a One-Dimensional Poroviscoelastic Column

Abstract

The response due to a dynamic loading of a poroviscoelastic one-dimensional column is treated analytically. Biot’s theory of poroelasticity is generalized to poroviscoelasticity using the elastic-viscoelastic correspondence principle in the Laplace domain. Damping effects of the solid skeletal structure and the solid material itself are taken into account. The fluid is modeled as in the original Biot’s theory without any viscoelastic effects. The solution of the governing set of two coupled differential equations known from the purely poroelastic case is converted to the poroviscoelastic solution using the developed elastic-viscoelastic correspondence in Laplace domain. The time-dependent response of the column is achieved by the “Convolution Quadrature Method” proposed by Lubich. Some interesting effects of viscoelasticity on the response of the column caused by a stress, pressure, and displacement loading are studied.