Geodesic
Method and some results of numerical estimation of effective Biot's coefficient of rocks
Čebyševskij sbornik, Tome 23 (2022) no. 4, pp. 382-393.

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In this article, a method and some results of the numerical estimation of effective Biot's coefficient of a porous material are described. The estimation is made by carrying out the calculation on a representative volume element (RVE) of the material. The outer boundary of the RVE is rigidly fixed, and pressure is applied to the surface of the pores. The elasticity boundary value problem with given boundary conditions is solved numerically, using the Russian CAE-system "Fidesys". The stress field obtained as a result of the solution is averaged over the volume. Effective Biot's coefficient is calculated from the averaged stress tensor. Comparison of the numerical results for the effective Biot coefficient with the analytical solution is carried out on the simplest model - a cube with a spherical pore. For different porosities and for different Poisson's ratios of the material, it is shown that the error is no more than 5%. Effective Biot's coefficient is also estimated for models with a more complex pore shape. Numerical results show the presence of significant anisotropy in obtained Biot's coefficients.
Keywords: theory of elasticity, poroelasticity, rock physics, homogenization, Biot's coefficient, numerical simulation. 
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M. Ya. Yakovlev; A. A. Semykin; V. A. Levin. Method and some results of numerical estimation of effective Biot's coefficient of rocks. Čebyševskij sbornik, Tome 23 (2022) no. 4, pp. 382-393. http://geodesic.mathdoc.fr/item/CHEB_2022_23_4_a29/

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