DOI QR코드

DOI QR Code

Optimal design of shape of a working in cracked rock mass

  • Mirsalimov, Vagif M. (Department of Mechanics, Azerbaijan Technical University)
  • 투고 : 2019.07.31
  • 심사 : 2021.01.20
  • 발행 : 2021.02.10

초록

A criterion and a method for solving a problem on the prevention of mine working fracture under the action of tectonic and gravitational forces are offered. Based on minimal criterion, theoretical analysis of the definition of the optimal shape of working in the rock mass weakened by arbitrarily located rectilinear cracks was carried out. A closed system of algebraic equations allowing to minimize the stress state and stress intensity factors depending on mechanical and geometrical characteristics of the rock, is constructed. The relation between the shape of the working and the stress intensity factors and also location and sizes of the cracks is obtained. The found optimal shape of working increases load-bearing capacity of the rock.

키워드

참고문헌

  1. Andreev, L.V. (1986), In the World of Shells, Mir, Moscow, Russia.
  2. Aitaliyev, Sh.M., Banichuk, N.V. and Kayupov, M.A. (1986), Optimal Design of Extended Underground Structures, Nauka, Alma-Ata, Kazakhstan.
  3. Banichuk, N.V. (1977), "Optimality conditions in the problem of seeking the hole shapes in elastic bodies", J. Appl. Math. Mech., 41(5), 946-951. https://doi.org/10.1016/0021-8928(77)90179-4.
  4. Banichuk, N.V. (1980), Shape Optimization of Elastic Solids, Nauka, Moscow, Russia.
  5. Barton, N. and Quadros, E. (2014), "Most rock masses are likely to be anisotropic", Proceedings of the ISRM Conference on Rock Mechanics for Natural Resources and Infrastructure-SBMR 2014, Goiania, Brazil, September.
  6. Burchill, M. and Heller, M. (2004), "Optimal free-form shapes for holes in flat plates under uniaxial and biaxial loading", J. Strain Anal. Eng. Des., 39(6), 595-614. https://doi.org/10.1243/0309324042379266.
  7. Chang, X., Ma, W., Li, Z. and Wang, H. (2018), "Crack behaviour of top layer in layered rocks", Geomech. Eng., 16(1), 49-58. https://doi.org/10.12989/gae.2018.16.1.049.
  8. Chen, Y., Zhang, X., Zhu, W. and Wang, W. (2018), "Modified discontinuous deformation analysis for rock failure: Crack propagation", Geomech. Eng., 14(4), 325-336. https://doi.org/10.12989/gae.2018.14.4.325.
  9. Cherepanov, G.P. (1963), "An inverse elastic-plastic problem under plane strain", Izvestija Akad. nauk SSSR. Otdelenie tehn. nauk. Mehanika i mashinostroenie, (2), 57-60.
  10. Cherepanov, G.P. (1966), "One inverse problem of elasticity theory", Mech. Solids, (3), 119-130.
  11. Cherepanov, G.P. (1974), "Inverse problems of the plane theory of elasticity", J. Appl. Math. Mech., 38(6), 915-931. https://doi.org/10.1016/0021-8928(75)90085-4.
  12. Сherepanov, G.P. (2015), "Optimum shapes of elastic bodies: Equistrong wings of aircrafts and equistrong underground tunnels", Phys. Mesomech., 18(4), 391-401. https://doi.org/10.1134/S1029959915040116.
  13. Givoli, D. and Elishakoff, I. (1992), "Stress concentration at a nearly circular hole with uncertain irregularities", J. Appl. Mech., 59(2S), S65-S71. https://doi.org/10.1115/1.2899509.
  14. Gogolauri, L. (2012), "The problem of finding equistrong holes in an elastic square", Proc. A. Razmadze Mathematical Institute, 158, 25-31.
  15. Hoek, E. and Brown, E.T. (1980), Underground Excavations in Rock, Institution of Mining and Metallurgy, London, England, U.K.
  16. Kalantarly, N.M. (2017), "Equal strength hole to inhibit longitudinal shear crack growth", J. Mech. Eng., 20(4), 31-37. https://doi.org/10.15407/pmach2017.04.031.
  17. Kirilyuk, V.S. and Levchuk, O.I. (2008), "On an inverse thermo-elasticity problem for an infinite medium containing a cavity of unknown shape", J. Eng. Math., 61(2-4), 219-229. https://doi.org/10.1007/s10665-007-9189-8.
  18. Kurshin, L.M. and Onoprienko P.N. (1976), "Determination of the shapes of doubly-connected bar sections of maximum torsional stiffness", J. Appl. Math. Mech., 40(6), 1020-1026. https://doi.org/10.1016/0021-8928(76)90144-1.
  19. Lee, J. and Hong, J.W. (2018), "Crack initiation and fragmentation processes in pre-cracked rock-like materials", Geomech. Eng., 15(5), 1047-1059. https://doi.org/10.12989/gae.2018.15.5.1047.
  20. Lv, H., Tang, Y., Zhang, L., Cheng, Z. and Zhang, Y. (2019), "Analysis for mechanical characteristics and failure models of coal specimens with non-penetrating single crack", Geomech. Eng., 17(4), 355-365. https://doi.org/10.12989/gae.2019.17.4.355.
  21. Mirsalimov, V.M. (1974), "On the optimum shape of apertures for a perforated plate subject to bending", J. Appl. Mech. Tech. Phys., 15(6), 842-845. https://doi.org/10.1007/BF00864606.
  22. Mirsalimov, V.M. (1975), "Converse problem of elasticity theory for an anisotropic medium", J. Appl. Mech. Tech. Phys., 16(4), 645-648. https://doi.org/10.1007/BF00858311.
  23. Mirsalimov, V.M. (1977), "Inverse doubly periodic problem of thermoelasticity", Mech. Solids, 12(4), 147-154.
  24. Mirsalimov, V.M. (1979), "A working of uniform strength in the solid rock", Soviet Mining, 15(4), 327-330. https://doi.org/10.1007/BF02499529.
  25. Mirsalimov, V.M. (1987), Non-one-dimensional Elastoplastic Problems, Nauka, Moscow, Russia.
  26. Mirsalimov, V.M. (2019), "Inverse problem of elasticity for a plate weakened by hole and cracks", Math. Prob. Eng. https://doi.org/10.1155/2019/4931489.
  27. Mirsalimov, V.M. (2020), "Minimizing the stressed state of a plate with a hole and cracks", Eng. Optimiz., 52(2), 288-302. https://doi.org/10.1080/0305215X.2019.1584619.
  28. Mir-Salim-zade, M.V. (2007), "Determination of equistrong hole shape in isotropic medium, reinforced by regular system of stringers", Materialy, tehnologii, instrumenty, 12(4), 10-14.
  29. Mir-Salim-zade, M.V. (2019), "Minimization of the stressed state of a stringer plate with a hole and rectilinear cracks", J. Mech. Eng., 22(2), 59-69. https://doi.org/10.15407/pmach2019.02.059.
  30. Muskhelishvili, N.I. (1977), Some Basic Problems of Mathematical Theory of Elasticity, Springer, Dordrecht, The Netherlands.
  31. Odishelidze, N., Criado-Aldeanueva, Criado, F.F. and Sanchez, J.M. (2016), "Stress concentration in an elastic square plate with a full-strength hole", Math. Mech. Solids, 21(5), 552-561. https://doi.org/10.1177/1081286514530753.
  32. Panasyuk, V.V., Savruk, M.P. and Datsyshyn, A.P. (1976), Stress Distribution around Cracks in Plates and Shells, Naukova Dumka, Kiev, Ukraine.
  33. Savruk, M.P. (1988), Stress Intensity Factors in Solids with Cracks, Naukova Dumka, Kiev, Ukraine.
  34. Savruk, M.P. and Kazberuk A. (2017), Stress Concentration at Notches. Springer, Cham, Switzerland.
  35. Savruk, M.P. and Kravets, V.S. (2002), "Application of the method of singular integral equations to the determination of the contours of equistrong holes in plates", Mater. Sci., 38(1), 34-46. https://doi.org/10.1023/A:1020116613794.
  36. Sheinin, V.I. (1972), "On the asymptotic method for calculating stress near rough surface of elastic solids", Mech. Solids, 7(2), 94-102.
  37. Sun, W., Du, H., Zhou, F. and Shao, J. (2019), "Experimental study of crack propagation of rock-like specimens containing conjugate fractures", Geomech. Eng., 17(4), 323-331. https://doi.org/10.12989/gae.2019.17.4.323.
  38. Vigdergauz, S.B. (1976), "Integral equation of the inverse problem of the plane theory of elasticity", J. Appl. Math. Mech., 40(3), 518-522. https://doi.org/10.1016/0021-8928(76)90046-0.
  39. Vigdergauz, S.B. (1977), "On a case of the inverse problem of two-dimensional theory of elasticity", J. Appl. Math. Mech., 41(5), 902-908. https://doi.org/10.1016/0021-8928(77)90176-9.
  40. Vigdergauz, S. (2006), "The stress-minimizing hole in an elastic plate under remote shear", J. Mech. Mater. Struct., 1(2), 387-406. https://doi.org/2140/jomms.2006.1.387. https://doi.org/10.2140/jomms.2006.1.387
  41. Vigdergauz, S. (2016), "A planar grained structure with a multiphase nested inclusion in a periodic cell: Elastostatic solution and the equi-stressness", Math. Mech. Solids, 21(6), 709-724. https://doi.org/10.1177/1081286514536084.
  42. Vigdergauz, S. (2017), "Equi-stress boundaries in two- and three-dimensional elastostatics: The single-layer potential approach", Math. Mech. Solids, 22(4), 837-851. https://doi.org/10.1177/1081286515615001.
  43. Vigdergauz, S. (2018), "Simply and doubly periodic arrangements of the equi-stress holes in a perforated elastic plane: The single-layer potential approach", Math. Mech. Solids, 23(5), 805-819. https://doi.org/10.1177/1081286517691807.
  44. Wang, S.J., Lu, A.Z., Zhang X.L. and Zhang N. (2018), "Shape optimization of the hole in an orthotropic plate", Mech. Based Des. Struct. Machines, 46(1), 23-37. https://doi.org/10.1080/15397734.2016.1261036.
  45. Wheeler, L.T. (1976), "On the role of constant-stress surfaces in the problem of minimizing elastic stress concentration", Int. J. Solids Struct., 12(11), 779-789. https://doi.org/10.1016/0020-7683(76)90042-1.
  46. Wheeler, L.T. (1992), "Stress minimum forms for elastic solids", Appl. Mech. Rev., 45(1), 1-12. https://doi.org/10.1115/1.3119743.
  47. Wu, Z. (2009), "Optimal hole shape for minimum stress concentration using parameterized geometry models", Struct. Multidisciplin. O., 37(6), 625-634. https://doi.org/10.1007/s00158-008-0253-4.
  48. Zeng, X., Lu, A. and Wang, S. (2020), "Shape optimization of two equal holes in an infinite elastic plate", Mech. Based Des. Struct. Machines, 48(2), 133-145. https://doi.org/10.1080/15397734.2019.1620111.
  49. Zhou, L., Zhu, Z., Liu, B. and Fan, Y. (2018), "The effect of radial cracks on tunnel stability", Geomech. Eng., 15(2), 721-728. https://doi.org/10.12989/gae.2018.15.2.721.
  50. Zhu, J.Q. and Yang, X.L. (2018), "Probabilistic stability analysis of rock slopes with cracks", Geomech. Eng., 16(6), 655-667. https://doi.org/10.12989/gae.2018.16.6.655.