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In this study, the dynamic response of a poroviscoelastic half-space to a transient surface load is investigated using Biot’s dynamic theory of poroelasticity and direct boundary element method. The skeleton of a porous material is assumed to be viscoelastic material. A model of a standard viscoelastic solid is applied to describe the viscoelastic properties of a skeleton. Viscoelastic effects are taken into account by means of the elastic-viscoelastic correspondence principle. The initial boundary-value problem is reduced to a boundary-value problem by formal application of the Laplace transform. In a first stage, the solution is obtained in the frequency domain. The transient solutions are obtained, in a second stage, by applying numerical inversion of the Laplace transform which is applied based on the Durbin algorithm with a variable frequency step to the previously synthesized frequency domain solutions. 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. A normal distributed uniform loading is applied over a rectangular region of the half-space surface, while the other parts are kept traction-free. The effect of the viscoelastic properties of the skeleton of a poroelastic material on vertical displacements on the half-space surface is investigated.

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The Response of Poroviscoelatic Layered Half-Space and Half-Space Weakened by Cavity to Transient Load by Boundary Element Approach

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  • 发表日期：

    2025年

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  • Andrey N. Petrov,
  • Leonid A. Igumnov,
  • Aleksandr A. Belov,
  • Valeriy V. Novikov

摘要

In this study, the dynamic response of a poroviscoelastic half-space to a transient surface load is investigated using Biot’s dynamic theory of poroelasticity and direct boundary element method. The skeleton of a porous material is assumed to be viscoelastic material. A model of a standard viscoelastic solid is applied to describe the viscoelastic properties of a skeleton. Viscoelastic effects are taken into account by means of the elastic-viscoelastic correspondence principle. The initial boundary-value problem is reduced to a boundary-value problem by formal application of the Laplace transform. In a first stage, the solution is obtained in the frequency domain. The transient solutions are obtained, in a second stage, by applying numerical inversion of the Laplace transform which is applied based on the Durbin algorithm with a variable frequency step to the previously synthesized frequency domain solutions. 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. A normal distributed uniform loading is applied over a rectangular region of the half-space surface, while the other parts are kept traction-free. The effect of the viscoelastic properties of the skeleton of a poroelastic material on vertical displacements on the half-space surface is investigated.