 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
|
| << Previous article | Volume 52, Issue 2 / 2017 | Next article >> |
| N.B. Artamonova, A.Zh. Mukatova, and S.V. Sheshenin, "Asymptotic Analysis of the Equilibrium Equation of a Fluid-Saturated Porous Medium by the Homogenization Method," Mech. Solids. 52 (2), 212-223 (2017) |
| Year |
2017 |
Volume |
52 |
Number |
2 |
Pages |
212-223 |
| DOI |
10.3103/S002565441702011X |
| Title |
Asymptotic Analysis of the Equilibrium Equation of a Fluid-Saturated Porous Medium by the Homogenization Method |
| Author(s) |
N.B. Artamonova (Lomonosov Moscow State University, Moscow, 119992 Russia, artamonovanb@mail.ru)
A.Zh. Mukatova (Lomonosov Moscow State University, Moscow, 119992 Russia)
S.V. Sheshenin (Lomonosov Moscow State University, Moscow, 119992 Russia) |
| Abstract |
The homogenization of static elasticity equations describing the stress strain state of fluid-saturated porous medium is considered. In this paper, the homogenization method is used to determine the pore pressure transfer tensor, which (a coefficient in the isotropic case) is an important parameter influencing the stress-strain state of fluid-saturated rocks. It shows what a part of the pressure in the fluid is "active" in the formation of macroscopic strains.
The pore pressure transfer tensor is calculated for model and real geological specimens. The dependence of this tensor on the porosity, pore shape, and Poisson ratio is investigated. The use of the computational technique for determining the effective properties of rocks shows that it is practically important in the engineering geology. |
| Keywords |
porous soil, effective stresses, asymptotic homogenization method, effective moduli of elasticity, pore pressure transfer tensor, Biot parameter, Eshelby solution |
| References |
| 1. | N. S. Bakhvalov and G. P. Panasenko, Homogenization of Processes in Periodic Media (Nauka, Moscow, 1984) [in Russian]. |
| 2. | B. E. Pobedrya,
Mechanics of Composite Materials
(Izdat. MGU, Moscow, 1984)
[in Russian]. |
| 3. | N. V. Melnikova, V. V. Rzhevskii, and M. M. Protod'yakonova (Editors),
Handbook (Cadastre) of Physical Properties of Rocks
(Nedra, Moscow, 1975)
[in Russian]. |
| 4. | S. P. Clark, Jr. (Editor),
Handbook of Physical Constants of Rocks
(Mir, Moscow, 1969)
[in Russian]. |
| 5. | N. B. Dortman (Editor),
Practical Handbook of Physical Properties of Rocks and Minerals (Petrophysics)
(Nedra. Moscow, 1975)
[in Russian]. |
| 6. | E. V. Kalinin, S. V. Sheshenin, and M. I. Bujakov,
"Variations in Stress Strain State of Rocks Composing the Valley Sides
under Seismic Actions,"
Vestnik Moskov. Univ. Ser. 4. Geologiya,
No. 6, 43-48 (1996)
[Moscow Univ. Geol. Bull. (Engl. Transl.)]. |
| 7. | S. V. Sheshenin, E. V. Kalinin, and M. I. Bujakov,
"Equivalent Properties of Rock Strata: Static and Dynamic Analysis,"
Int. J. Numeric. Analyt. Meth. Geomech.
21 (8), 569-579 (1997), |
| 8. | J. G. Wang, C. F. Leung, and Y. Ichikawa,
"A simplified Homogenization Method for Composite Soils,"
Comput. Geotech.,
29 (6), 477-500 (2002). |
| 9. | G. Hassen, M. Gueguin, and P. de Buhan,
"A Homogenization Approach for Assessing the Yield Strength Properties
of Stone Column Reinforced Soils,"
Eur. J. Mech. A/Solids
37, 266-280 (2013). |
| 10. | V. I. Gorbachev, "Homogenization of Linear Problems in the
Mechanics of Composites with Nonperiodic Inhomogeneities," Izv.
Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 31-37 (2001) [Mech.
Solids (Engl. Transl.) 36 (1), 24-29 (2001)]. |
| 11. | C. H. Cheng,
"Crack Models for a Transversely Anisotropic Medium,"
J. Geophys. Res. Solid Earth
98 (B1), 675-684 (1993). |
| 12. | J. D. Eshelby,
"The Determination of the Elastic Field on an Ellipsoidal Inclusion and Related Problems,"
Proc. Roy. Soc. London. Ser. A
241 (1226), 376-396 (1957). |
| 13. | M. A. Biot,
"General Theory of Three-Dimensional Consolidation,"
J. Appl. Phys.
12, 155-164 (1941). |
| 14. | J. Geertama,
"The Effect of Fluid Pressure Decline on Volumetric Changes of Porous Rocks,"
Trans. AIME
210, 331-339 (1957). |
| 15. | M. A. Biot and D. G. Willis,
"The Elastic Coefficients of the Theory of Consolidation,"
J. Appl. Phys.
24, 594-601 (1957). |
| 16. | I. Fatt,
"Compressibility of Sandstones at Low to Moderate Pressures,"
AAPG Bull.
42 (8), 1924-1957 (1958). |
| 17. | A. W. Skempton,
"Effective Stress in Soils, Concrete and Rocks,"
in Proc. of Conf. on Pore Pressure and Suction in Soils
(Butterworth, London, 1960),
pp. 4-16. |
| 18. | D. E. Ochs, H. Y. Chen, and L. W. Teufer,
"Relating in Situ Stresses and Transient Pressure Testing for a Fractured Well,"
Paper SPE 38674 Presented at the Annual Technical Conference & Exhibition, San Antonio, 1997,
pp. 301-316. |
| 19. | Y. Gueguen and M. Bouteca,
Mechanics of Fluid-Saturated Rocks
(Elsevier Acad. Press, 2004). |
| 20. | E. M. Chesnokov, M. Ammerman, S. Sinha, and Y. A. Kukharenko,
"Tensor Character of Biot Parameters in Poroelastic Anisotropic Media under Stress:
Static and Dynamic Cases,"
in Proc. 2nd Int. Workshop Rainbow in the Earth, Berkley, California, 2005
(2005). |
| 21. | V. M. Dobrynin,
Physical Properties of Oil-Gas Collectors in Long Holes
(Nedra, Moscow, 1965)
[in Russian]. |
| 22. | A. Nur and J. D. Byerlee,
"An Exact Effective Stress Law for Elastic Deformation of Rock with Fluids,"
J. Geophys. Res.
76 (26), 6414-6419 (1971). |
| 23. | M. A. Addis,
"The Stress-Depletion Response of Reservoirs,"
in Proc. of 1997 SPE Annual Technical Conference and Exhibition. Pt. 1. Formation Evolution and Reservoir Geology. Sam Antonio, 1997,
pp. 55-65. |
| 24. | M. A. Biot,
"Mechanics of Deformation and Acoustic Propagation in Porous Media,"
J. Appl. Phys.
33, 1482-1498 (1962). |
| 25. | M. M. Carroll,
"An Effective Stress Law for Anisotropic Elastic Deformation,"
J. Geoph. Res. Solid Earth
84 (B13), 7510-7512 (1979). |
| 26. | M. Thompson and J. R. Willis,
"A Reformulation of the Equations of Anisotropic Poroelasticity,"
J. Appl. Phys.
58, 612-616 (1991). |
| 27. | C. C. Mei,
"Micro-Scale Basis of Seepage Flow. Theory of Homogenization,"
in Lectures Notes on Fluid Dynamics, Ch. 6.2
(2002), pp. 1-7. |
| 28. | S. V. Sheshenin and M. I. Savenkova,
"Homogenization of Nonlinear Problems in the Mechanics of Composites,"
Vestnik Moskov. Univ. Ser. I Mat. Mekh.
67 (5), 58-62 (2012)
[Moscow Univ. Meth. Bull. (Engl. Transl.)
67 (5), 126-130 (2012)]. |
| 29. | R. M. Christensen,
Introduction to Mechanics of Composite Materials
(Wiley, New York, 1979; Mir, Moscow, 1982). |
| 30. | Yu. V. Frolova,
"Patterns of Transformations in the Compositions and Properties of Icelandic Hyaloclastites during Lithogenesis,"
Vestnik Moskov. Univ. Ser. IV. Geolog.,
No. 2, 45-55 (2010)
[Moscow Univ. Geol. Bull. (Engl. Transl.)
65 (2), 104-114 (2010)]. |
|
| Received |
10 November 2014 |
| Link to Fulltext |
|
| << Previous article | Volume 52, Issue 2 / 2017 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English