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Year 2019, Volume 9, Issue 4, 712 - 723, 01.12.2019

Abstract

References

  • [1] Alexandrov, A. V., Potapov, V. D., (1975), Fundamentals of the theory of elasticity and plasticity, Vyshaya shkola, Moskva, 400 p.
  • [2] Bezukhov, N. I., (1975), Basic theory of elasticity, plasticity and creep. Vyshaya shkola, Moskva, 512 p.
  • [3] Connell, L. D., (2012), Coupled flow and geomechanical processes during gas production from coal seams, Int. J. of Coal Geolgy, 79(1-2), pp. 18-28. doi: 10.1016/j.coal.2009.03.008
  • [4] Coussy, O., (2010), Mechanics and Physics of Porous Solids, John Wiley & Son Ltd, 281 p.
  • [5] Djadkov, P. G., Mel’nikov, V. I., Nazarov, L. A., Nazarova, L. A., San’kov, V. A., (1999), Increase of seismotectonic activity in the Baikal region in 1989-95: results of experimental observation and numerical modeling of changes in the stress strained state, Geol. Geofiz., 40(3), pp. 373-386 . [6] Eltsov, I. N., Nazarov, L. A., Nazarova, L. A., Nesterova, G. V., Epov, M. I., (2012) Logging Interpretation into Account Hydrodynamical and Geomechanical Processes in an Invaded Zone. Dokl. Earth Sci., 445(2), pp. 1021-1024. doi: 10.1134/S1028334X1208020X
  • [7] Goldberg, V. M., Skvortsov, N. P., Lukyanchikova, N., (1994), Underground disposal of industrial waste water. Nedra, Moskva, 282 p.
  • [8] Guo, X., Du, Z., Li, S., (2003), Computer modeling and simulation of coalbed methane reservoir, Paper SPE 84815 in SPE Eastern Regional/AAPG Eastern Section Joint Meeting, Pittsburgh.
  • [9] Karchevsky, A. L., (2016), Calculation of Stresses in a Coal Seam in Presence of Gas Diffusion, J. Appl. Industrial Math., 10(4), pp. 482-493. doi: 10.1134/S1990478916040049
  • [10] Khalilov, S. A., (1977), On a system of coordinate functions for solving boundary value problems in the theory of plates and shells. In: Strength of aircraft structures, KhAI, Kharkov, 4, pp. 60-65.
  • [11] Khalilov, S. A., (1978), New systems of orthonormal polynomials, some of their properties and applications. In: Strength of aircraft structures, KhAI, Kharkov, 5, pp. 46-56.
  • [12] Khalilov, S. A., (1982): Solution in rectangle of static problem of elasticity for given stresses on the border. In: Questions of design of aircraft structures, KhAI, Kharkov, 3, pp. 120-127.
  • [13] Khalilov, S. A., (1984), Calculation of some definite integrals containing the attached Legendre functions of the second and fourth orders. In: Strength of aircraft structures, KhAI, Kharkov, 7, pp. 158-165.
  • [14] Khalilov, S. A., Mintyuk, V. B., Tkachenko, D. A., (1984), Construction and investigation of the approximate analytical solutions biharmonic problem in the rectangle at the top of homogeneous boundary conditions. Aerospace Engineering and Technology, 2, pp. 40-49.
  • [15] Khalilov, S. A., Mintyuk, V. B., Tkachenko, D. A., (2013), Approximate analytical solution of the biharmonic problem in a rectangle with homogeneous main boundary conditions on two opposite sides and arbitrary - in other. Aerospace Engineering and Technology, 5, pp. 40-49.
  • [16] Khalilov, S. A., Mintyuk, V. B., Tkachenko, D. A., (2011) The construction and study of analytical and numerical solution of the problem of bending of a rigidly fixed rectangular plate, Open information and computer integrated technologies, 49, pp. 81-94.
  • [17] Khalilov, S. A., Mintyuk, V. B., Tkachenko, D. A., Kopychko, V. V., (2014), Own spectrum of biharmonic operator in the rectangle with the main boundary conditions, Aerospace Engineering and Technology, 5, pp. 70-78.
  • [18] Khalilov, S. A., Krivtsov, V. S., Mintyuk, V. B., Tkachenko, D. A., (2015), The Green’s function of fundamental boundary value problem for the biharmonic operator in a rectangle, Aerospace Engineering and Technology, 6, pp. 12-22.
  • [19] Kiselev, V. A., (1975), Plane problem of elasticity theory. Vyshaya shkola, Moskva, 151 p.
  • [20] Kravets, Y. A., (2009), Improved recovery hydrophobic reservoir by injection into the reservoir salted water, Vestnik OAO NK “Rosneft’ ”, 4, pp. 34-38.
  • [21] Liang, B., Lu, X., (1999), Coupling Numerical Analysis of Seepage Field and Stress Field for the Rock Mass with Fracture, J. Water Res. Water Eng., 20(4), pp. 14-16.
  • [22] Mintyuk, V. B., (2007), Orthonormal basis for the one-dimensional boundary value problems. Aerospace Engineering and Technology, 5, pp. 32-36.
  • [23] Nazarov, L. A., Nazarova, L. A., (1999), Some Geomechanical Aspects of Gas Recovery from Coal Seams, J. Min. Sci., 35 (2), pp. 135-145 .
  • [24] Nazarov, L. A., Nazarova, L. A., Yaroslavtsev, A.F., Miroshnichenko, N.A., Vasil’eva, E.V., (2011), Evolution of stress fields and induced seismicity in operating mines, J. Min. Sci., 47(6), pp. 707-713. doi: 10.1134/S1062739147060013
  • [25] Nowacki, W., (1975), Theory of elasticity, Mir, Moskva, 872 p.
  • [26] Puchkov, L. A., Slastunov, S. V., Kolikov, K. S., (2002), Extraction of methane from coal seams, Moscow State Mining University, Moskva, 389 p.
  • [27] Samul’, I. N., (1975), Basic of the theory of elasticity and plasticity. Vyshaya shkola, Moskva, 264 p.
  • [28] Seidle, J., (2011), Fundamentals of Coalbed Methane Reservoir Engineering, PennWell Books, 416 p.
  • [29] Tarona, J., Elsworth, D., Min, K.-B., (2009), Numerical simulation of thermal-hydrologic-mechanicalchemical processes in deformable, fractured porous media, Int. J. Rock Mech. Min. Sci., 46(5), pp. 842-854. doi: 10.1016/j.ijrmms.2009.01.008
  • [30] Tkachenko, D. A., (2014), Orthonormal in the energy space of the biharmonic operator in a rectangle basis with homogeneous boundary conditions on the main border. Aerospace Engineering and Technology, 3, pp. 41-51.
  • [31] Urbancic, T. I., Trifu, C.-I., (2000), Recent advances in seismic monitoring technology at Canadian mines, J. Appl. Geophys., 45(4), pp. 225-237. doi: 10.1016/S0926-9851(00)00030-6
  • [32] Zhenbi, L., Baiting, Z., (2012), Microseism Monitoring System for Coal and Gas Outburst, Int. J. Computer Science Issues, 9(5), pp. 24-28. http://www.ijcsi.org/papers/IJCSI-9-5-1-24-28.pdf
  • [33] Zhuang, X., Huang, R., Liang, C., Rabczuk, T., (1999), A Coupled Thermo-Hydro-Mechanical Model of Jointed Hard Rock for Compressed Air Energy Storage, Math. Prob. Eng., ID 179169. doi: 10.1155/2014/179169

CALCULATION OF STRESSES IN A WATERED LAYER

Year 2019, Volume 9, Issue 4, 712 - 723, 01.12.2019

Abstract

In the paper the analitical expressions for computing stresses in a watered layer have been obtained. It is not required to solve endless systems of equations.

References

  • [1] Alexandrov, A. V., Potapov, V. D., (1975), Fundamentals of the theory of elasticity and plasticity, Vyshaya shkola, Moskva, 400 p.
  • [2] Bezukhov, N. I., (1975), Basic theory of elasticity, plasticity and creep. Vyshaya shkola, Moskva, 512 p.
  • [3] Connell, L. D., (2012), Coupled flow and geomechanical processes during gas production from coal seams, Int. J. of Coal Geolgy, 79(1-2), pp. 18-28. doi: 10.1016/j.coal.2009.03.008
  • [4] Coussy, O., (2010), Mechanics and Physics of Porous Solids, John Wiley & Son Ltd, 281 p.
  • [5] Djadkov, P. G., Mel’nikov, V. I., Nazarov, L. A., Nazarova, L. A., San’kov, V. A., (1999), Increase of seismotectonic activity in the Baikal region in 1989-95: results of experimental observation and numerical modeling of changes in the stress strained state, Geol. Geofiz., 40(3), pp. 373-386 . [6] Eltsov, I. N., Nazarov, L. A., Nazarova, L. A., Nesterova, G. V., Epov, M. I., (2012) Logging Interpretation into Account Hydrodynamical and Geomechanical Processes in an Invaded Zone. Dokl. Earth Sci., 445(2), pp. 1021-1024. doi: 10.1134/S1028334X1208020X
  • [7] Goldberg, V. M., Skvortsov, N. P., Lukyanchikova, N., (1994), Underground disposal of industrial waste water. Nedra, Moskva, 282 p.
  • [8] Guo, X., Du, Z., Li, S., (2003), Computer modeling and simulation of coalbed methane reservoir, Paper SPE 84815 in SPE Eastern Regional/AAPG Eastern Section Joint Meeting, Pittsburgh.
  • [9] Karchevsky, A. L., (2016), Calculation of Stresses in a Coal Seam in Presence of Gas Diffusion, J. Appl. Industrial Math., 10(4), pp. 482-493. doi: 10.1134/S1990478916040049
  • [10] Khalilov, S. A., (1977), On a system of coordinate functions for solving boundary value problems in the theory of plates and shells. In: Strength of aircraft structures, KhAI, Kharkov, 4, pp. 60-65.
  • [11] Khalilov, S. A., (1978), New systems of orthonormal polynomials, some of their properties and applications. In: Strength of aircraft structures, KhAI, Kharkov, 5, pp. 46-56.
  • [12] Khalilov, S. A., (1982): Solution in rectangle of static problem of elasticity for given stresses on the border. In: Questions of design of aircraft structures, KhAI, Kharkov, 3, pp. 120-127.
  • [13] Khalilov, S. A., (1984), Calculation of some definite integrals containing the attached Legendre functions of the second and fourth orders. In: Strength of aircraft structures, KhAI, Kharkov, 7, pp. 158-165.
  • [14] Khalilov, S. A., Mintyuk, V. B., Tkachenko, D. A., (1984), Construction and investigation of the approximate analytical solutions biharmonic problem in the rectangle at the top of homogeneous boundary conditions. Aerospace Engineering and Technology, 2, pp. 40-49.
  • [15] Khalilov, S. A., Mintyuk, V. B., Tkachenko, D. A., (2013), Approximate analytical solution of the biharmonic problem in a rectangle with homogeneous main boundary conditions on two opposite sides and arbitrary - in other. Aerospace Engineering and Technology, 5, pp. 40-49.
  • [16] Khalilov, S. A., Mintyuk, V. B., Tkachenko, D. A., (2011) The construction and study of analytical and numerical solution of the problem of bending of a rigidly fixed rectangular plate, Open information and computer integrated technologies, 49, pp. 81-94.
  • [17] Khalilov, S. A., Mintyuk, V. B., Tkachenko, D. A., Kopychko, V. V., (2014), Own spectrum of biharmonic operator in the rectangle with the main boundary conditions, Aerospace Engineering and Technology, 5, pp. 70-78.
  • [18] Khalilov, S. A., Krivtsov, V. S., Mintyuk, V. B., Tkachenko, D. A., (2015), The Green’s function of fundamental boundary value problem for the biharmonic operator in a rectangle, Aerospace Engineering and Technology, 6, pp. 12-22.
  • [19] Kiselev, V. A., (1975), Plane problem of elasticity theory. Vyshaya shkola, Moskva, 151 p.
  • [20] Kravets, Y. A., (2009), Improved recovery hydrophobic reservoir by injection into the reservoir salted water, Vestnik OAO NK “Rosneft’ ”, 4, pp. 34-38.
  • [21] Liang, B., Lu, X., (1999), Coupling Numerical Analysis of Seepage Field and Stress Field for the Rock Mass with Fracture, J. Water Res. Water Eng., 20(4), pp. 14-16.
  • [22] Mintyuk, V. B., (2007), Orthonormal basis for the one-dimensional boundary value problems. Aerospace Engineering and Technology, 5, pp. 32-36.
  • [23] Nazarov, L. A., Nazarova, L. A., (1999), Some Geomechanical Aspects of Gas Recovery from Coal Seams, J. Min. Sci., 35 (2), pp. 135-145 .
  • [24] Nazarov, L. A., Nazarova, L. A., Yaroslavtsev, A.F., Miroshnichenko, N.A., Vasil’eva, E.V., (2011), Evolution of stress fields and induced seismicity in operating mines, J. Min. Sci., 47(6), pp. 707-713. doi: 10.1134/S1062739147060013
  • [25] Nowacki, W., (1975), Theory of elasticity, Mir, Moskva, 872 p.
  • [26] Puchkov, L. A., Slastunov, S. V., Kolikov, K. S., (2002), Extraction of methane from coal seams, Moscow State Mining University, Moskva, 389 p.
  • [27] Samul’, I. N., (1975), Basic of the theory of elasticity and plasticity. Vyshaya shkola, Moskva, 264 p.
  • [28] Seidle, J., (2011), Fundamentals of Coalbed Methane Reservoir Engineering, PennWell Books, 416 p.
  • [29] Tarona, J., Elsworth, D., Min, K.-B., (2009), Numerical simulation of thermal-hydrologic-mechanicalchemical processes in deformable, fractured porous media, Int. J. Rock Mech. Min. Sci., 46(5), pp. 842-854. doi: 10.1016/j.ijrmms.2009.01.008
  • [30] Tkachenko, D. A., (2014), Orthonormal in the energy space of the biharmonic operator in a rectangle basis with homogeneous boundary conditions on the main border. Aerospace Engineering and Technology, 3, pp. 41-51.
  • [31] Urbancic, T. I., Trifu, C.-I., (2000), Recent advances in seismic monitoring technology at Canadian mines, J. Appl. Geophys., 45(4), pp. 225-237. doi: 10.1016/S0926-9851(00)00030-6
  • [32] Zhenbi, L., Baiting, Z., (2012), Microseism Monitoring System for Coal and Gas Outburst, Int. J. Computer Science Issues, 9(5), pp. 24-28. http://www.ijcsi.org/papers/IJCSI-9-5-1-24-28.pdf
  • [33] Zhuang, X., Huang, R., Liang, C., Rabczuk, T., (1999), A Coupled Thermo-Hydro-Mechanical Model of Jointed Hard Rock for Compressed Air Energy Storage, Math. Prob. Eng., ID 179169. doi: 10.1155/2014/179169

Details

Primary Language English
Journal Section Research Article
Authors

A. R. DZHANDİGULOV This is me
L. Gumilyov Eurasian National University, St. Satpayev, 2, 010000, Astana, Republic of Kazakhstan.


A. L. KARCHEVSKY This is me
Sobolev Institute of Mathamatics SO RAN, pr. Koptyga, 4, 630090 Novosibirsk, Russia

Publication Date December 1, 2019
Published in Issue Year 2019, Volume 9, Issue 4

Cite

Bibtex @ { twmsjaem760939, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2019}, volume = {9}, number = {4}, pages = {712 - 723}, title = {CALCULATION OF STRESSES IN A WATERED LAYER}, key = {cite}, author = {Dzhandigulov, A. R. and Karchevsky, A. L.} }