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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{CHEB_2022_23_4_a29,
     author = {M. Ya. Yakovlev and A. A. Semykin and V. A. Levin},
     title = {Method and some results of numerical estimation of effective {Biot's} coefficient of rocks},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {382--393},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2022_23_4_a29/}
}
TY  - JOUR
AU  - M. Ya. Yakovlev
AU  - A. A. Semykin
AU  - V. A. Levin
TI  - Method and some results of numerical estimation of effective Biot's coefficient of rocks
JO  - Čebyševskij sbornik
PY  - 2022
SP  - 382
EP  - 393
VL  - 23
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2022_23_4_a29/
LA  - ru
ID  - CHEB_2022_23_4_a29
ER  - 
%0 Journal Article
%A M. Ya. Yakovlev
%A A. A. Semykin
%A V. A. Levin
%T Method and some results of numerical estimation of effective Biot's coefficient of rocks
%J Čebyševskij sbornik
%D 2022
%P 382-393
%V 23
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2022_23_4_a29/
%G ru
%F CHEB_2022_23_4_a29
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/