Year 2019,
Volume 9,
Issue 4,
712 - 723,
01.12.2019
A. R. DZHANDİGULOV
A. L. KARCHEVSKY
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
A. R. DZHANDİGULOV
A. L. KARCHEVSKY
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