Calculation of stresses in a~coal seam in presence of gas diffusions

A. L. Karchevskii

Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 4, pp. 31-43.

Résumé

We obtain the analitical expressions for computing stresses in a coal seam taking into account the diffusion of the gas. The solution is presented as a sum whose four terms are convergent series. All functions in the expressions can easily be computed either separately or successively; i.e, it is not required to solve infinite systems of equations.

Détail

Keywords: stress, plane problem of elasticity theory, biharmonic equation.

Bibliographie

[1] Puchkov L. A., Slastunov S. V., Kolikov K. S., Izvlechenie metana iz ugolnykh plastov, Izd-vo Mosk. gos. gornogo un-ta, M., 2002

[2] Zakharov V. N., Seismoakusticheskoe prognozirovanie i kontrol sostoyaniya i svoistv gornykh porod pri razrabotke ugolnykh mestorozhdenii, izd. IGD im. A. A. Skochinskogo, M., 2002

[3] Zhenbi L., Baiting Zh., “Microseism monitoring system for coal and gas outburst”, Internat. J. Computer Sci. Issues, 9:5, No 1 (2012), 24–28

[4] Zhurkov S. N., “K voprosu o fizicheskoi osnove prochnosti”, Fizika tverdogo tela, 22:11 (1985), 3344–3349

[5] Li T. B., Xiao X. P., “Comprehensive integrated methods of rockburst prediction in underground engineering”, Adv. Earth Sci., 23:5 (2008), 533–540

[6] Nazarov L. A., Nazarova L. A., Yaroslavtsev A. F., Miroshnichenko N. A., Vasileva E. V., “Evolyutsiya geomekhanicheskikh polei i tekhnogennaya seismichnost pri otrabotke mestorozhdenii poleznykh iskopaemykh”, Fiziko-tekhn. problemy razrabotki poleznykh iskopaemykh, 2010, no. 6, 6–13

[7] Amusin B. Z., Fadeev A. B., Metod konechnykh elementov pri reshenii zadach gornoi geomekhaniki, Nedra, M., 1975

[8] Zienkiewicz O. C., Taylor R. L., The Finite Element Method for Solid and Structural Mechanics, Elsevier, 2005 | Zbl

[9] Dyadkov P. G., Nazarov L. A., Nazarova L. A., “Chislennoe modelirovanie napryazhennogo sostoyaniya zemnoi kody i uslovii vozniknoveniya dinamicheskoi neustoichivosti seismoaktivnykh razlomov pri riftogeneze”, Geologiya i geofizika, 38:12 (1997), 2001–2010

[10] Nazarov L. A., Nazarova L. A., “Nekotorye geomekhanicheskie aspekty problemy izvlecheniya gaza iz ugolnykh plastov”, Fiziko-tekhn. problemy razrabotki poleznykh iskopaemykh, 1999, no. 2, 35–44

[11] Novatskii V., Teoriya uprugosti, Mir, M., 1975 | MR

[12] Aleksandrov A. V., Potapov V. D., Osnovy teorii uprugosti i plastichnosti, Vyssh. shkola, M., 1990

[13] Bezukhov N. A., Osnovy teorii uprugosti, plastichnosti i polzuchesti, Vyssh. shkola, M., 1968

[14] Kiselev V. A., Ploskaya zadacha teorii uprugosti, Vyssh. shkola, M., 1976

[15] Samul V. A., Osnovy teorii uprugosti i plastichnosti, Vyssh. shkola, M., 1982

[16] Khalilov S. A., “Ob odnoi sisteme koordinatnykh funktsii dlya resheniya kraevykh zadach teorii plastin i obolochek”, Prochnost konstruktsii letatelnykh apparatov, 4, izd. KhAI, Kharkov, 1977, 60–65

[17] Khalilov S. A., “Novye sistemy ortonormirovannykh mnogochlenov, nekotorye ikh svoistva i prilozheniya”, Prochnost konstruktsii letatelnykh apparatov, 5, izd. KhAI, Kharkov, 1978, 46–56

[18] Khalilov S. A., “Vychislenie nekotorykh opredelennykh integralov, soderzhaschikh prisoedinennye funktsii Lezhandra vtorogo i chetvertogo poryadkov”, Prochnost konstruktsii letatelnykh apparatov, 7, izd. KhAI, Kharkov, 1984, 158–165

[19] Khalilov S. A., Mintyuk V. B., Tkachenko D. A., “Postroenie i issledovanie priblizhennogo analiticheskogo resheniya bigarmonicheskoi problemy v pryamougolnike pri odnorodnykh glavnykh kraevykh usloviyakh”, Aviatsionno-kosmicheskaya tekhnika i tekhnologiya, 2010, no. 2, 40–49

[20] Khalilov S. A., Mintyuk V. B., Tkachenko D. A., “Priblizhennoe analiticheskoe reshenie bigarmonicheskoi problemy v pryamougolnike pri odnorodnykh glavnykh kraevykh usloviyakh na dvukh protivopolozhnykh storonakh i proizvolnykh – na drugikh”, Aviatsionno-kosmicheskaya tekhnika i tekhnologiya, 2010, no. 5, 40–49

[21] Khalilov S. A., Mintyuk V. B., Tkachenko D. A., “Postroenie i issledovanie analitiko-chislennogo resheniya zadachi ob izgibe zhestko zaschemlennoi pryamougolnoi plastiny”, Otkrytye informatsionnye i kompyuternye integrirovannye tekhnologii, 2011, no. 49, 81–94

[22] Khalilov S. A., Mintyuk V. B., Tkachenko D. A., Kopychko V. V., “Sobstvennyi spektr bigarmonicheskogo operatora v pryamougolnike pri glavnykh kraevykh usloviyakh”, Aviatsionno-kosmicheskaya tekhnika i tekhnologiya, 2014, no. 5, 70–78

[23] Khalilov S. A., Krivtsov V. S., Mintyuk V. B., Tkachenko D. A., “Funktsiya Grina osnovnoi kraevoi zadachi dlya bigarmonicheskogo operatora v pryamougolnike”, Aviatsionno-kosmicheskaya tekhnika i tekhnologiya, 2015, no. 6, 12–22

[24] Mintyuk V. B., “Ortonormirovannyi bazis dlya odnomernykh kraevykh zadach”, Aviatsionno-kosmicheskaya tekhnika i tekhnologiya, 2007, no. 5, 32–36

[25] Tkachenko D. A., “Ortonormirovannyi v energeticheskom prostranstve bigarmonicheskogo operatora bazis v pryamougolnike pri odnorodnykh glavnykh kraevykh usloviyakh po granitse”, Aviatsionno-kosmicheskaya tekhnika i tekhnologiya, 2014, no. 3, 41–51

[26] Prudnikov A. P., Brychkov Yu. A., Marichev O. A., Integraly i ryady, v. 1, Elementarnye funktsii, Fizmatlit, M., 2002 | MR