# Peculiarities of wave propagation processes in poroelastic media

## DOI:

https://doi.org/10.32347/2410-2547.2020.105.247-254## Keywords:

poroelasticity, porous media, boundary integral equations, fundamental solution## Abstract

During analyzing of wave propagation processes in the fluid-saturated porous media unlike the theory of elasticity should be applied proposed by Biot the two phase model of media in which porous the solid elements are belonging to the first phase and the elements of pores fluid filler are belong to the second phase. Sometimes, for solving problems three phase model are used in which porous skeleton is partially saturated by fluid and partially saturated by gas. For the elastic porous media are introduced parameters such as: the porosity, the fluid viscosity, the permeability, the Biot coefficient of effective stress, the shear modulus and the bulk modulus, the mass densities and the total density of the porous material. Also the fundamental characteristic of the porous media is propagation of three different compression waves: the longitudinal fast wave, the second longitudinal slow wave, and the third transversal slow wave. One of the methods that are used for solving problems of poroelasticity is the Boundary Integral Equation Method. The algorithmic bases of it are the boundary analogues of Somiliani’s formulas for the solid displacements and the fluid pressure. The boundary integral equations and the fundamental solutions that are comprised in the poroelastic equations are different from the theory of elasticity analogues because the body with fluid-saturated pores is differ from the continuous homogeneous elastic media. Figures show that the graphs for the poroelastic region may be gradual approximated to the elastic analogues during changing some parameters. The biggest influence for displacements functions has change of the parameter R especially gradual increase of it for the some order. When for changing the functions graphs of the generalized derivatives one gradual increase of the parameter Q for one order is enough.

## References

Ehlers W. Foundations of multiphasic and porous materials / W.Ehlers, J.Bluh // Porous Media: Theory, Experiments and Numerical Applications, Springer, Berlin. – 2002. – P. 3–8.

Frenkel Ya.I. К teorii seysmicheskih b seysmoelektricheskih yavleniy vo vlaghnoy pochve / Ya.I.Frenkel // Izv. AS USSR. Cer. Geografiya i geophisika. – 1984. – Т.8, № 4. – P. 133-150.

Biot M.A. Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-Frequency Range / M.A.Biot // J. Acoust. Soc. Amer. – 1956. – V. 28, № 2. – P.168-178.

Biot M.A. The elastic coefficients of the theory of consolidation / M.A.Biot, D.G.Willis // J. Appl. Mechanics. – 1957. – P. 594-601.

Yew C.H. The determination of Biot parameters for sandstone / C.H.Yew, P.N.Jogi // Experimental Mechanics. – 1978. – №.19. – P. 167-177.

Detournay E. Fundamentals of poroelasticity. Chapter 5 in Comprehensive Rock Engineering: Principles, Practice and Projects / E Detournay., A.H.-D.Cheng // Analysis and Design Method / ed. By C.Fairhurst. // Pergamon Press. – 1993. – V.II. – P. 113-171.

Nikolaevskiy V.N. Mehanika poristyh i treshchinovatyh sred (Mechanics of porous and fractured media)/ V.N.Nikolaevskiy – М.:Nedra, 1984. – P. 233.

Torraca G. Porous Building Materials: materials science for architectural conservation / G.Torraca. – Rome: ICCROM, 2005. – P.149.

Dominguez J. Boundary elements in dynamics / J.Dominguez. – Computational Mechanics Publications. Southampton Boston, 1993. – 689 p.

Cheng A.H.-D. Integral equations for dynamic poroelasticity in frequency domain with boundary element solution / A.H.-D.Cheng, T. Badmus, D.E. Beskot // J. Eng. Mech., ASCE. – V. 117. – P. 1136-1157.

Schanz M. Wave propogation in viscoelastic and poroelastic continua / M. Schanz. − Berlin: Springer, 2001. –170 p.

Li P. Boundary element method for wave propagation in partially saturated poroelastic continua / P.Li. - Verlag der Technischen Universität Graz, 2012. – 143 p.

Igumnov L.A. Chislenno-analiticheskoe modelirovanie dinamiki tryehmernyh sostavnyh porouprugih tel (Numerical-analytical modeling of dynamic three-dimensional composite poroelastic bodies). [electronic study-methodical manual] / L.A. Igumnov, C.Y. Litvinchuk, A.V. Amenickiy., A.A. Belov. – Nighniy Novgorod: University of Nighniy Novgorod, 2012. – 52 p.

Laplace domain 3D dynamic fundamental solutions of unsaturated soils: the 4th International Conference on Geotechnical Engineering and Soil Mechanics, 2-3 November 2010, Tehran, Iran / I.Ashayeri, M.Kamalian, M.K.Jafari. – P. 1-8, № 40.

Manolis G.D. Integral formulation and fundamental solutions of dynamic poroelasticity and thermoelasticity / G.D.Manolis, D.E.Beskos // Acta Mechanica. − 1989. − № 76. − P. 89-104.

Vorona Yu.V. Propagation of cylindrical waves in poroelastic media / Yu.V.Vorona, Каrа І.D. // Strength of Materials and Theory of Structures. – 2014. – № 93. – P. 146-152.

Kovtun Al.A. Poverhnosnye volny na granice uprugo-poristoy sredy i gydkosti / Al.A.Rovtun // Voprosy geofiziki (Problems of geophysics). – 2013. – Vol. 46. – P. 14-25.

Bonnet G. Basic singular solution for a poroelastic medium in the dynamic range / G.Bonnet // J. Acoust. Soc. Amer. – 1987. – V. 82. – P. 1758-1762.

Kara I.D. Numerical solution of the problem of porous solids vibration // Strength of Materials and Theory of Structures. – 2017. – № 99. – P. 193–202.

Sorokin K.E. Chislennoe resheniye lineynoy dvumernoy dynamicheskoy zadachi dlya poristyh sred (Numerical solution of a linear two-dimensional dynamic problem for porous media)/ К.E.Sorokin, H.H.Imomnazarov // Journal of Siberian Federal University. Mathematics & Physics. – 2010. – № 3(2). – P. 256-261.

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