# Stressed-deformed state of two drifts in a tiltly layered cracked array in the conditions of elastic deformations of rocks

### Abstract

In the study, based on a homogeneous anisotropic mechanical-mathematical mo del of an inclined,finely layered array with a bip erio dic system of slots, the patterns of distribution of elastic stresses and displacements near two drifts of arbitrary profile shap e and depth by the finite elementmetho d under conditions of plane deformation have b een systematically numerically investigated.The calculation was carried out by converting weakened ro cks with two excavations in elasticity toan equivalent homogeneous medium. It is difficult to solve the problem of the initial static stressstate of two-diagonal workings on a ro ck weakened by two-p erio d cracks by the analogous metho d,therefore it was solved by the generalized metho d of plane deformation using the first and secondisoparametric elements by the finite element metho d. Metho ds for dividing the area sp ecified bythe finite element metho d into parametric quadrangular elements and numerically determining thestress-strain state of double workings are given.A computational algorithm has b een develop ed and a software package has b een develop ed forstudying the elastic state of adjacent cavities of arbitrary depth and shap e. A multivariate numerical calculation and analysis of the influence on the comp onents of stresses and displacements nearcavities, geometrical, physical parameters of ro cks was carried out.### References

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[10] Yerzhanov Zh.S. and Karimbaev T.D., "The finite element method in problems of rock mechanics" , Alma-Ata: Nauka (1975): 238.

[11] Aitaliev Sh.M., Masanov Zh.K., Baymakhanov I.B. and Makhmetova N.M., "Seismic stress state of paired tunnels" , Computational methods for solving the problems of mechanics of a deformable solid Karaganda (1987): 3-15.

[12] Jean-Michel H., "Hydrodynamics of Free Surface Flows" , Modeling with the Finite Element Method 1st Edition The USA (2007): 360.

[13] Mahmetova N.M., Solonenko V.G. and Bekzhanova S.T., "The calculation of free oscillations of an anisotropic threedimensional array of underground structures" , Bul letin of National Academy of Sciences of the Republic of Kazakhstan (2017): 24-28.

[14] Khoei A.E., and Haghighat, "Extended finite element modeling of deformable porous media with arbitrary interfaces" ,

Applied Mathematical Modeling (2011): 5426-5441.

[15] Iktisanov V., "Hydrodynamic research methods and modeling of multilateral horizontal wells" , Publishing house (2007): 56.

[16] Khodabakhshi G., Spataru C., "Development of a predictive mathematical model for fluid-porous media interaction

problems" , Supplement Proceedings of ICMI (2006): 123-138.

[17] Vu M., Sulem J., Subrin D., Monin M., "Semi-Analytical Solution for Stresses Mathematical Model of Fluid Filtration to Horizontal Well 211 and Displacements in a Tunnel Excavated in Transversely Isotropic Formation with Non-Linear Behavior" , Rock Mechanics (2013): 213-229.

[18] Wang H.F., "Princeton University Press: Theory of linear poroelasticity with applications to geo mechanics and hydrogeology" , New Jersey (2000), 276.

[19] Ali E., Guang W., Zhiming Zh., Weixue J., "Assessments of Strength Anisotropy and Deformation Behavior of Banded Amphibolite Rocks" , Geotechnical Geological Engineering (2014): 429-438.

[20] Wittke W., Ernst and Sohn GmbH., "Ro ck Mechanics Based on an Anisotropic Jointed Ro ck Mo del" , New-York (2014): 875.

[21] Alabi O.O., Ajah D.T. and Abidoye L.K., "Mathematical Modeling of Hydraulic Conductivity in Homogeneous Porous Media: Influence of Porosity and Implications in Subsurface Transport of Contaminants" , Electronic Journal of Geotechnical Engineering (2016): 89-102.

[2] Stocke K., "Fur das Gebingsdruckproblem wichtige Begriffe aus der technischen Mechanik" , Zeitschrift fur des BergHutten und Salinenwesen Bd. 84, H. 11(1937): 465-67.

[3] Muskhelishvili N.I., "Some basic tasks of the mathematical theory of elasticity" , Moscow: Nauka (1966): 707.

[4] Filshtinsky L.A., "Stresses in Regular Double-Periodic Lattices" , Journal of Engineering. Solid Mechanics (1967): 112.

[5] Cosmodamian A.S.,Neskorodev M.M., "The double-periodic problem for an anisotropic medium weakened by elliptical

holes" , Dopovidi AN URSR ser. A (1970): 148.

[6] Yerzhanov Zh.S., Kaydarov K.K. and Tusupov M.T., "A mountain massif with incomplete adhesion of layers" , Mechanical

processes in a mountain massif Alma-Ata, Nauka (1969): 115.

[7] Erzhanov Zh.S., Aitaliev Sh.M. and Masanov J.K., "Stability of horizontal workings in an inclined-layered massif" , AlmaAta, Nauka (1971): 160.

[8] Segerlind L., "Application of the finite element method" , M.: Mir (1979): 392.

[9] Amusin B.Z. and Fadeev A.V., "The finite element method in solving problems of mining mechanics" , M.: Nedra (1975): 142.

[10] Yerzhanov Zh.S. and Karimbaev T.D., "The finite element method in problems of rock mechanics" , Alma-Ata: Nauka (1975): 238.

[11] Aitaliev Sh.M., Masanov Zh.K., Baymakhanov I.B. and Makhmetova N.M., "Seismic stress state of paired tunnels" , Computational methods for solving the problems of mechanics of a deformable solid Karaganda (1987): 3-15.

[12] Jean-Michel H., "Hydrodynamics of Free Surface Flows" , Modeling with the Finite Element Method 1st Edition The USA (2007): 360.

[13] Mahmetova N.M., Solonenko V.G. and Bekzhanova S.T., "The calculation of free oscillations of an anisotropic threedimensional array of underground structures" , Bul letin of National Academy of Sciences of the Republic of Kazakhstan (2017): 24-28.

[14] Khoei A.E., and Haghighat, "Extended finite element modeling of deformable porous media with arbitrary interfaces" ,

Applied Mathematical Modeling (2011): 5426-5441.

[15] Iktisanov V., "Hydrodynamic research methods and modeling of multilateral horizontal wells" , Publishing house (2007): 56.

[16] Khodabakhshi G., Spataru C., "Development of a predictive mathematical model for fluid-porous media interaction

problems" , Supplement Proceedings of ICMI (2006): 123-138.

[17] Vu M., Sulem J., Subrin D., Monin M., "Semi-Analytical Solution for Stresses Mathematical Model of Fluid Filtration to Horizontal Well 211 and Displacements in a Tunnel Excavated in Transversely Isotropic Formation with Non-Linear Behavior" , Rock Mechanics (2013): 213-229.

[18] Wang H.F., "Princeton University Press: Theory of linear poroelasticity with applications to geo mechanics and hydrogeology" , New Jersey (2000), 276.

[19] Ali E., Guang W., Zhiming Zh., Weixue J., "Assessments of Strength Anisotropy and Deformation Behavior of Banded Amphibolite Rocks" , Geotechnical Geological Engineering (2014): 429-438.

[20] Wittke W., Ernst and Sohn GmbH., "Ro ck Mechanics Based on an Anisotropic Jointed Ro ck Mo del" , New-York (2014): 875.

[21] Alabi O.O., Ajah D.T. and Abidoye L.K., "Mathematical Modeling of Hydraulic Conductivity in Homogeneous Porous Media: Influence of Porosity and Implications in Subsurface Transport of Contaminants" , Electronic Journal of Geotechnical Engineering (2016): 89-102.

Published

2020-04-06

How to Cite

AZHIKHANOV, N. T. et al.
Stressed-deformed state of two drifts in a tiltly layered cracked array in the conditions of elastic deformations of rocks.

**Journal of Mathematics, Mechanics and Computer Science**, [S.l.], v. 105, n. 1, p. 120-128, apr. 2020. ISSN 2617-4871. Available at: <https://bm.kaznu.kz/index.php/kaznu/article/view/712>. Date accessed: 07 june 2020.
Section

Mechanics

Keywords
drift, isoparametric element, transtropic array, finite element method