Modeling Surface Waves on a Partially Saturated Poroelastic Half-Space

• Leonid Igumnov
• Svetlana Litvinchuk
• Andrey Petrov
• Igor Vorobtsov
Conference paper
Part of the Structural Integrity book series (STIN, volume 8)

Abstract

Defining relations for a partially saturated porous Biot medium, written in the variables of displacements of the skeleton and pore pressures of the fillers, are considered. The initial system of partial differential equations includes five functions (a displacement vector and two pore pressures). The model of the material corresponds to a three-component medium. A system of equations in partial derivatives and boundary-value conditions are written in Laplace transform for time variable and in direct time with initial conditions. The boundary-value problem is analyzed using the method of boundary integral equations, their solutions being sought with the boundary-element method. The numerical scheme is based on using the Green-Bettie-Somigliana formula. Quadratic interpolation polynoms are taken as form functions in describing the boundary of the body. Unknown boundary fields are sought through nodal values in interpolation nodes. The element-by-element numerical integration uses Gauss method and an adaptive integration algorithm. The boundary-element schemes are constructed, based on the consistent approximation of the boundary functions and the collocation method. The solution of the formulated system of linear algebraic equations is sought using the block-type Gauss method. The boundary integral equation method in combination with the technique of searching a boundary-element solution is oriented at a dynamic problem of an isotropic homogeneous partially saturated poroelastic half-space. The time-stepping method for numerical inverting the Laplace transform is used to obtain the solution in the time domain.

Keywords

Poroelasticity Biot’s theory Boundary integral equation Time-Step method

References

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Li, P., Schanz, M.: Time domain boundary element formulation for partially saturated poroelasticity. Eng. Anal. Boundary Elem. 37(11), 1483–1498 (2013)
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Goldshteyn, R.V.: Boundary Integral Equations Method: Numerical Aspects & Application in Mechanics. Mir, Moscow (1978)Google Scholar
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Lubich, C.: Convolution quadrature and discretized operational calculus. I Numerische Mathematik 52(2), 129–145 (1988)
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Belov, A., Amenitskiy, A., Litvinchuk, S., Petrov, A.: Boundary-element analysis if the problem of a prismatic body acting on a half-space in a porous-elastic formulation. Probl. Strength Plast. 74, 154–159 (2012)

© Springer Nature Switzerland AG 2019

Authors and Affiliations

• Leonid Igumnov
• 1
• Svetlana Litvinchuk
• 1
• Andrey Petrov
• 1
• Igor Vorobtsov
• 1
1. 1.National Research Lobachevsky State University of Nizhny NovgorodNizhny NovgorodRussia

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