Mô Hình ĐGradient Biến Dạng Cục Bộ của Khối Đá Gần Các Đường Hầm Sâu

Shemyakin, E.I., Fisenko, G.N., Kurlenya, M.V., Oparin, V.N., et al., The Rock-Mass Zone Disintegration near Deep Level Mining Opening. Part I: Data of In Situ Observations, J. Min. Sci., 1986, vol. 22, no. 3, pp. 3–13. Tan, Y.L., Ning, J.G., and Li, H.T., In Situ Explorations on Zonal Disintegration of Roof Strata in Deep Coalmines, Int J. Rock Mech. Min. Sci., 2012, vol. 49, pp. 113–124. Shemyakin, E.I., Fisenko, G.N., Kurlenya, M.V., Oparin, V.N., et al., The Rock-Mass Zone Disintegration near Deep Level Mining Opening. Part II: The Fracture of Rock in Models From Equivalent Materials, J. Min. Sci., 1986, vol. 22, no. 4, pp. 3–15. Shemyakin, E.I., Fisenko, G.N., Kurlenya, M.V., Oparin, V.N., et al., The Rock-Mass Zone Disintegration near Deep Level Mining Opening. Part III: Theoretical Representation, J. Min. Sci., 1987, vol. 23, no. 1, pp. 3–8. Shemyakin, E.I., Kurlenya, M.V., Oparin, V.N., Reva, V.N., et al., The Rock-Mass Zone Disintegration near Deep Level Mining Opening. Part IV: Practical Application, J. Min. Sci., 1989, vol. 25, no. 4, pp. 3–9. Kurlenya, M.V., Oparin, V.N., Bobrov, G.F., et al., On Splitting Effect in Zones of Supporting Pressure, J. Min. Sci., 1995, vol. 31, no. 5, pp. 3–11. Gu, J.C., Gu, L.Y., and Chen, A.M., Model Test Study on Mechanism of Layered Fracture within Surrounding Rock of Tunnels in Deep Stratum, Chinese Journal of Rock Mechanics and Engineering, 2008, vol. 27, no. 5, pp. 433–4384. Zhang, Q.Y., Chen, X.G., Lin, B., et al., Study of 3D Geomechanical Model Test of Zonal Disintegration of Surrounding Rock of Deep Tunnel, Chinese J Rock Mech. Eng., 2009, vol. 28, no. 9, pp. 1757–1766. Chanyshev, A.I., On Problem of Fracture of Deformable Media. Part I: Basic Equations, J. Min. Sci., 2001, vol. 37, no. 2, pp. 273–288. Chanyshev, A.I., On Problem of Fracture of Deformable Media. Part. II: Discussion of Results of Analytical Solutions, J. Min. Sci., 2001, vol. 37, no. 3, pp. 392–400. Gusev, M.A. and Paroshin, A.A., Non-Euclidian Model of Rock-Mass Zone Disintegration near Underground Mining Opening, Appl. Mech. and Tech. Phys., 2001, Vvl. 42, no. 1, pp. 147–156. Oparin, V.N., Tapsiev, A.P., Rozenbaum, M.A., et al., Zonal’naya dezintegratsiya gornykh porod i ustoichivost’ podzemnykh vyrabotok (Zonal Disintegration of Rock Mass and Stability of Underground Openings), Novosibirsk: SO RAN, 2008. Jirasek, M. and Rolshoven, S., Localization Properties of Strain Softening Gradient Plasticity. Part I: Strain Gradient Theories, Int. J. Solids Struct., 2009, vol. 46, pp. 2225–2238. Jirasek, M. and Rolshoven, S., Localization Properties of Strain Softening Gradient Plasticity. Part II: Theories with Gradients of Internal Variables, Int. J. Solids Struct., 2009, vol. 46, pp. 2239–2254. Toupin, R.A., Elastic Materials with Couple Stresses, Arch. Ration Mech. Anal., 1962, vol. 11, no. 1, pp. 385–414. Mindlin, R.D., Second Gradient of Strain and Surface Tension in Linear Elasticity, Int. J. Solids Struct., 1965, vol. 28, pp. 845–857. Eshel, N. and Rosenfeld, G., Axi-Symmetric Problems in Elastic Materials of Grade two, J. Franklin Inst., 1975, vol. 299, no. 1, pp. 43–51. Fleck, N.A. and Hutchinson, J.W., Strain Gradient Plasticity, Advances in Applied Mechanics, 1997, vol. 33, pp. 295–361. Gurtin, M.E., A Gradient Theory of Single Crystal Visco-Plasticity that Accounts for Geometrically Necessary Dislocations, J. Mech. Phys. Solids, 2002, vol. 50, pp. 5–32. Aifantis, E.C., On the Microstructural Origin of Certain Inelastic Models, J. Eng. Mater. Tech., 1984, vol. 106, pp. 326–330. Aifantis, E.C., Pattern Formation in Plasticity, Int. J. Eng. Sci., 1995, vol. 33, pp. 2161–2178. Polizzotto, C., Unified Thermodynamic Framework for Nonlocal/Gradient Continuum Theories, Eur. J. Mech. A/Solids, 2003, vol. 17, no. 3, pp. 651–668. Abu Al-Rub, R.K., Voyiadjis, G.Z., and Bammann, J.B., A Thermodynamic Based Higher-Order Gradient Theory for Size Dependent Plasticity, Int. J. Solids Struct., 2007, vol. 44, pp. 2888–2923. Fleck, N.A. and Willis, J.R., A Mathematical Basis for Strain-Gradient Plasticity Theory. Part II: Tensorial Plastic Multiplier, J. Mech. Phys. Solids, 2009, vol. 57, pp. 1045–1057. Wang, M.Y., Qi, C.Z., Qian, Q.H., and Chen, J.J., One plastic Gradient Model of Zonal Disintegration of Rock Mass near Deep Level Tunnels, J. Min. Sci., 2012, vol. 48, no. 1, pp. 54–62. Ilyushin, A.A., Plastichnost’ (Plasticity), Moscow–Leningrad: OGIZ, 1948. Baklashov, I.V. and Kartozia, B.A., Mekhanika podzemnykh sooruzhenii i konstruktsiui krepei (Mechanics of Underground Stuctures and Support), Moscow: Nedra, 1984. Zhao, J.D., Sheng, D.C., and Sloan, S.W., Cavity Expansion of a Gradient-Dependent Solid Cylinder, Int. J. Solids Struct., 2007, vol. 44, pp. 4342–4368. Keller, H.B., Numerical Methods for Two-Point Boundary-Value Problems, Blaisdell Pub. Co., Waltham, Massachusetts, 1968, pp. 61–68. Chambon, R. and Moullet, J.C., Uniqueness Studies in Boundary Value Problems Involving Some Second Gradient Models, Comp. Methods Appl. Mech. Eng., 2004, vol. 193, pp. 2771–2796.