Open AccessBEM ANALYSIS OF WAVE PROPAGATION IN POROVISCOELASTIC LAYERED HALFSPACE AND HALFSPACE WITH CAVITY
Author(s) -
A. A. Ipatov
Publication year - 2020
Publication title -
problemy pročnosti i plastičnosti
Language(s) - English
Resource type - Journals
ISSN - 1814-9146
DOI - 10.32326/1814-9146-2020-82-3-364-376
Subject(s) - poromechanics , viscoelasticity , biot number , laplace transform , mathematical analysis , discretization , mathematics , boundary element method , boundary value problem , half space , quadrature (astronomy) , finite element method , porous medium , mechanics , porosity , physics , geology , geotechnical engineering , optics , thermodynamics
The paper is dedicated to the wave propagation a porous-viscoelastic material. As a mathematical model of a fully saturated poroelastic medium, we consider the Biot model with four basic functions – pore pressure and skeleton movements. The Biot model is supplemented by the principle of elastic and viscoelastic reaction correspondence. The skeleton of a porous material is assumed to be viscoelastic material. A model of a standard viscoelastic solid is spplied to describe the viscoelastic properties of a skeleton. The initial boundary-value problem is reduced to a boundary-value problem by formal application of the Laplace transform. To solve boundary integral equations, the boundary element method is performed. Quadrangular eight-node biquadratic elements are used for boundary element discretization. Numerical integration is carried out according to Gaussian quadrature formulas using algorithms for lowering the order and eliminating features. To obtain a solution in explicit time, numerical inversion of the Laplace transform is applied based on the Durbin algorithm with a variable frequency step.This study is a development of the existing boundary-element technique for solving problems on layered porous-elastic half-spaces. This will allow you to take into account the heterogeneity of the soil in depth. The problem of the action of a vertical force in the form of the Heaviside function on the surface of a layered porous-elastic half-space and a half-space with a cavity is considered. Variants of a homogeneous and heterogeneous half-space are considered. Under the model of heterogeneity we understand the piecewise homogeneous solid. The responses of the boundary displacements on the surface of the half-space are presented. The effect of the viscoelastic material model parameter on the dynamic response of displacements is demonstrated. It is established that the viscosity parameters have a significant effect on the nature of the distribution of parameters of wave processes.