Study of wave propagation in poroviscoelastic halfspace under normal harmonic load via BEM

Aleksandr Ipatov,Svetlana Litvinchuk,E Buzaud,A Cosculluela,H Couque,E Cadoni

doi:10.1051/epjconf/201818301029

Aleksandr Ipatov, Svetlana Litvinchuk + Show 4 more

Open Access

https://doi.org/10.1051/epjconf/201818301029

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Abstract

The present research is dedicated to a problem of a soil dynamics in case when media is subjected to a normal harmonic load. Such type of load may be observed for example because of working wind generator, and the aim is to create a model of possible impact. One of the most appropriate ways for soil modelling is the Biot model of poroelastic media and its enhancements. In this paper we treat a soil as a poroviscoelastic media. Our poroviscoelastic formulation is based on Biot theory of poroelasticity and correspondence principle applied to skeleton of porous material. Standard linear solid model is employed to describe viscoelastic media properties. Boundary integral equations method is applied to solving threedimensional boundary-value problems. The solution of the original problem is constructed in Laplace transforms, with the subsequent application of the algorithm for numerical inversion. To introduce BEdiscretization, we consider the regularized boundary-integral equation. Mixed boundary element discretization is introduced to obtain discrete analogues. Modified Durbin’s algorithm of numerical inversion of Laplace transform is used. Research is also dedicated to development of numerical modeling technique based on Boundary Element Method (BEM) in Laplace domain of solution three dimensional poroviscodynamic problems. Numerical example of a poroviscoelastic halfspace under harmonic load is considered. Viscoelastic model parameter influence on dynamic responses of boundary functions is studied. The comparison of transient responses is presented.

Highlights

Wave motion in porous media is an important issue in several branches of engineering science
Shanz and Cheng [14] presented an analytical solution in the Laplace domain and analytical time-domain solution without considering viscous coupling effect, and governing equations was extended for saturated poroviscoelastic media by using the Kelvin–Voigt model and obtained an analytical solution in the Laplace domain for the 1D problem [15]
A Laplace domain Boundary Element Method (BEM) formulation based on integral representations of the fundamental solutions has been presented for the analysis of three-dimensional anisotropic elastodynamic problems

Summary

Introduction

Wave motion in porous media is an important issue in several branches of engineering science. Time domain solutions are approximated by a modified Durbin’s numerical Laplace transform inversion routine. The Laplace transform is the main method for solving threedimensional transient problems in porous media. Modified Durbin’s algorithm of numerical inversion of Laplace transform is applied to perform solution in time domain. Shanz and Cheng [14] presented an analytical solution in the Laplace domain and analytical time-domain solution without considering viscous coupling effect, and governing equations was extended for saturated poroviscoelastic media by using the Kelvin–Voigt model and obtained an analytical solution in the Laplace domain for the 1D problem [15]. In present work we modify basic equations for fluidsaturated porous media proposed by Biot by replacing the classical linear elastic model of the solid skeleton with the viscoelastic model.

Problem statement

Boundary element formulation

Laplace transform inversion

Test example

Numerical example

Concluding remarks