Establishing the fundamentals of the theory of stability of mine workings

International Applied Mechanics

Volumn 39, Issue 1, 2003, Pages 20-48

  Guz, A N ^a  

^a S P TIMOSHENKO INSTITUTE OF MECHANICS   (Ukraine)

Author keywords

Closed cavities; Stability; Three dimensional theory; Underground mine workings

Indexed keywords

MINE WORKINGS; ROCK MODELS;

COMPRESSIVE STRESS; DEFORMATION; FRACTURE; ROCK MECHANICS; STABILITY; STRAIN; STRESS ANALYSIS; STRESS CONCENTRATION; UNDERGROUND MINE TRANSPORTATION;

MINES;

EID: 0038065337     PISSN: 10637095     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1023659931802     Document Type: Article

References (99)

1. Zh. S. Akopyan, "On nonaxisymmetric instability of a vertical mine working," Prikl. Mekh., 12, No. 5, 116-119 (1976).
2. Zh. S. Akopyan, "Numerical solution of a nonaxisymmetric stability problem for a vertical mine working," Prikl. Mekh., 12, No. 9, 130-131 (1976).
3. Zh. S. Akopyan, I. Yu. Babich, A. N. Guz, and L. V. Deriglazov, "On stability problems for vertical mine workings in an anisotropic rock mass, " Prikl. Mekh., 14, No. 12, 23-29 (1978).
4. Zh. S. Akopyan, I. Yu. Babich, A. N. Guz, and A. V. Navoyan, "Stability analysis of horizontal and vertical mine workings," Teor. Prikl. Mekh., 12, 99-103 (1981).
5. Zh. S. Akopyan and A. N. Guz, "On the variational principles of the theory of stability of mine workings for compressible models," Dokl. AN USSR, Ser. A, No. 1, 33-35 (1981).
6. Zh. S. Akopyan and A. N. Guz, "On the variational principles of the theory of stability of mine workings for incompressible models," Dokl. AN USSR, Ser. A, No. 10, 27-30 (1981).
7. Zh. S. Akopyan, A. N. Guz, and A. V. Navoyan, "On stability problems for vertical mine workings," Prikl. Mekh., 10, No. 5, 54-72 (1974).
8. Zh. S. Akopyan, A. N. Guz, and A. V. Navoyan, "Constructing the theory of stability of mine workings," Prikl. Mekh., 18, No. 5, 3-22 (1982).
9. M. T. Alimzhanov, "On stability of a horizontal underground working of circular cross section," Izv. AN Kaz. SSR, Ser. Fiz. Mat., 5, 80-86 (1967).
10. M. T. Alimzhanov, "On stability of a vertical shaft," in: Proc. Sum. Sci. Conf. on Mathematics and Mechanics [in Russian], Nauka, Alma-Ata (1967).
11. M. T. Alimzhanov, "Stability analysis of underground mine workings," in: Proc. 1st Sci. Conf. Young Scient. Acad. Sci. Sov. Rep. Kazakh. [in Russian], Nauka, Alma-Ata (1968), pp. 7-8.
12. M. T. Alimzhanov, "Stability analysis of horizontal underground workings," in: Problem of Rock Mechanics [in Russian], Nauka, Novosibirsk (1971), pp. 39-41.
13. M. T. Alimzhanov, Stability of the Equilibrium of Bodies and Problems of Rock Mechanics [in Russian], Nauka, Alma-Ata (1982).
14. M. T. Alimzhanov and N. A. Evstropov, "Stability analysis of underground cavities due to internal explosions," in: Trans. Moscow Institute of Mining [in Russian], Izd. MGI, Moscow (1971), pp. 20-25.
15. M. T. Alimzhanov and L. V. Ershov, "Stability of the equilibrium of bodies and some problems of rock pressure," in: Problems in Solid Mechanics [in Russian], Sudostroenie, Leningrad (1970), pp. 47-54.
16. M. T. Alimzhanov and L. V. Ershov, "On rock pressure pattern near a single permanent horizontal deep mine working," in: Problems in Rock Mechanics [in Russian], Nauka, Alma-Ata (1972), pp. 66-76.
17. M. T. Alimzhanov and M. D. Ishakov, "On stability of equilibrium and some axisymmetric problems of rock," in: Problems in Rock Mechanics [in Russian], Nauka, Alma-Ata (1972), pp. 243-255.
18. F. M. Asamidinov, "Stability of the rock mass near an elliptic horizontal mine working under uniaxial compression," Prikl. Mekh., 13, No. 11, 124-126 (1977).
19. F. M. Asamidinov, "Stability of the rock mass near an elliptic horizontal mine working under uniaxial tension," Tr. USKhA, 195, 74-76 (1977).
20. F. M. Asamidinov, A. N. Guz, and G. G. Kuliev, "On stability of noncircular horizontal mine workings," Prikl. Mekh., 10, No. 5, 54-62 (1974).
21. F. M. Asamidinov and G. G. Kuliev, "Stability of the rock near a square horizontal working," Prikl. Mekh., 16, No. 4, 125-128 (1980).
22. I. Yu. Babich, G. N. Baklanova, and A. N. Guz, "Plane elastoplastic stability problem for horizontal mine workings," Prikl. Mekh., 14, No. 3, 68-73 (1978).
23. I. Yu. Babich, G. N. Baklanova, and V. M. Nazarenko, "On stability of elastoplastic rock mass with a horizontal cavity under a linearized theory," in: Stress-Strain State of Rock Mass in Mountain Areas [in Russian], Frunze (1985), pp. 134-136.
24. I. Yu. Babich and A. N. Guz, "Rock instability as a possible outburst mechanism," Prikl. Mekh., 13, No. 5, 23-26 (1977).
25. I. Yu. Babich, A. N. Guz, and S. B. Lobovik, "On stability of an elastoplastic half-space around a spherical cavity," Prikl. Mekh., 14, No. 12, 23-29 (1978).
26. I. Yu. Babich and A. V. Navoyan, "Stability of a circular horizontal mine working," Prikl. Mekh., 13, No. 7, 112-116 (1977).
27. G. N. Baklanova, "On stability of horizontal workings under elastoplastic deformations," in: Proc. 2nd Rep. Conf. Young Scient. on Mechanics (Kiev, 1979) [in Russian], Naukova Dumka, Kiev (1979), pp. 12-13.
28. G. N. Baklanova, "Stability of elastoplastic rock around a horizontal mine working," in: Proc. All-Union Conf. of Young Experts on Construction of Hydroelectric Power Stations in Mountain Areas [in Russian], Metsniereba, Tbilisi (1979), pp. 27-28.
29. G. N. Baklanova, "Spatial stability problem for mine workings under elastoplastic deformations," Prikl. Mekh., 16, No. 7, 35-40 (1980).
30. G. N. Baklanova, "Study into the influence of the plastic properties of rock on the stability of mine workings," in: Proc. All-Union Conf. of Young Experts on Construction of Hydroelectric Power Stations in Mountain Areas [in Russian], Metsniereba, Tbilisi (1982), pp. 49-50.
31. G. N. Baklanova, "On the influence of the plastic properties of rock on the stability of a horizontal mine working," Prikl. Mekh., 19, No. 3, 120-124 (1983).
32. G. N. Baklanova and L. V. Deriglazov, "Stability of anisotropic rock mass near two horizontal mine workings," Prikl. Mekh., 28, No. 2, 60-63 (1992).
33. A. N. Guz, Stability of Three-Dimensional Deformable Bodies [in Russian], Naukova Dumka, Kiev (1971).
34. A. N. Guz, "On stability problems in rock mechanics," in: Problems in Rock Mechanics [in Russian], Nauka, Alma-Ata (1972), pp. 27-35.
35. A. N. Guz, Fundamentals of the Theory of Stability of Mine Workings [in Russian], Naukova Dumka, Kiev (1977).
36. A. N. Guz, "On the variational principles of the three-dimensional theory of stability of deformable bodies under follower loads," Dokl. AN SSSR, 246, No. 6, 1314-1316 (1979).
37. A. N. Guz, "The variational principles of the three-dimensional theory of stability of deformable bodies under a follower load," Prikl. Mekh., 15, No. 10, 24-30 (1979).
38. A. N. Guz, "On stability problems for mine workings," Dokl. AN SSSR, 253, No. 3, 553-555 (1980).
39. A. N. Guz, "Implementing variational methods in linear mechanical problems for multiply connected domains," Dokl. AN USSR, Ser. A, 4, 39-43 (1981).
40. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies [in Russian], Vyshcha Shkola, Kiev (1986).
41. A. N. Guz, "Developing the theory of stability of mine workings," Problems in Solid and Rock Mechanics (on the Occasion of the 70th Anniversary of Prof. L. V. Ershov) [in Russian], Izd. MGU, Moscow (2001), pp. 197-212.
42. A. N. Guz and I. Yu. Babich, Three-Dimensional Theory of Stability of Deformable Bodies, Vol. 4 of the six-volume series Spatial Problems of the Theory of Elasticity and Plasticity [in Russian], Naukova Dumka, Kiev (1985).
43. A. N. Guz and L. V. Deriglazov, "On stability of anisotropic rock near two parallel horizontal mine workings," Dokl AN SSSR, 325, No. 3, 450-454 (1992).
44. A. N. Guz and G. G. Kuliev, "Borehole stability theory revisited," Prikl. Mekh., 19, No. 3, 10-17 (1983).
45. A. N. Guz and A. V. Navoyan, "Stability analysis of a horizontal mine working of circular cross section," Dop. AN URSR, Ser. A, 7, 630-633 (1973).
46. A. N. Guz and V. N. Chekhov, "The linearized stability equations in study of folding in the earth's crust," in: Abstracts of Papers Read at the 5th Kazakhst. Interuniv. Sci. Conf. on Mathematics and Mechanics [in Russian], Pt. 2, Nauka, Alma-Ata (1974), pp. 141-143.
47. A. N. Guz and V. N. Chekhov, "Linearized theory of crustal folding," Prikl. Mekh., 11, No. 1, 3-14 (1975).
48. A. N. Guz and V. N. Chekhov, "Surface buckling of a laminated half-plane with elastoplastic deformation of layers," Dokl. AN SSSR, 272, No. 3, 546-550 (1983).
49. A. N. Guz and V. N. Chekhov, "Variational methods in stability problems for laminated semibounded media," Dokl. AN SSSR, 283, No. 5, 1123-1126 (1985).
50. L. V. Deriglazov, "Stability of a horizontal mine working in orthotropic rock mass," Prikl. Mekh., 13, No. 4, 45-49 (1977).
51. L. V. Deriglazov, "Stability of mine workings in transversely isotropic rock mass," Prikl. Mekh., 13, No. 5, 27-33 (1977).
52. L. V. Deriglazov, "Stability of a horizontal mine working in orthotropic rock mass under nonuniform compression," Prikl. Mekh., 15, No. 2, 99-102 (1979).
53. L. V. Deriglazov, "A note on the stability of the rock near two horizontal mine workings," Prikl. Mekh., 25, No. 3, 39-43 (1989).
54. L. V. Deriglazov, "Stability of the rock near two horizontal mine workings," Prikl. Mekh., 26, No. 3, 18-22 (1990).
55. L. V. Deriglazov, "On stability of the rock near two horizontal mine workings under nonuniform compression," Prikl. Mekh., 26, No. 6, 118-121 (1990).
56. L. V. Deriglazov, "Stability of multiply connected anisotropic rock," Prikl. Mekh., 29, No. 3, 56-59 (1993).
57. L. V. Deriglazov, V. B. Medvedev, and N. N. Svirkov, "On stability of the rock near two horizontal workings," Teor. Prikl. Mekh., 22, 16-20 (1991).
58. A. N. Dinnik, Papers on Mining [in Russian], Ugletekhizdat, Moscow (1957).
59. Zh. S. Erzhanov and A. K. Egorov, Theory of Rock Folding (a Mathematical Description) [in Russian], Nauka, Alma-Ata (1968).
60. Zh. S. Erzhanov, A. K. Egorov, I. A. Garagash et al., Theory of Crustal Folding [in Russian], Nauka, Moscow (1975).
61. L. V. Ershov, "Formulating stability problems for mine workings," Dokl. AN SSSR, 143, No. 2, 305-307 (1962).
62. L. V. Ershov, "Manifestation of rock pressure in horizontal mine working," Dokl. AN SSSR, 145, No. 2, 298-300 (1962).
63. L. V. Ershov, "Manifestation of rock pressure in a vertical mine shaft," Izv. AN SSSR, Otd. Tekhn. Nauk, 2, 103-107 (1962).
64. L. V. Ershov, "Artificial strengthening of pillars by supporting bars," Izv. AN SSSR, Otd. Tekhn. Nauk, 2, 180-182 (1963).
65. L. V. Ershov, "Study of rock pressure manifestation in the context of the stability of elastoplastic bodies," Prikl. Mekh., 9, No. 4, 387-397 (1963).
66. L. V. Ershov, "The mathematical theory of rock pressure revisited," in: Analytical Methods for Study into and Mathematical Simulation of Rock Processes [in Russian], Gosgortekhizdat, Moscow (1963), pp. 19-43.
67. L. V. Ershov and V. A. Maksimov, Mathematical Fundamentals of Rock Physics [in Russian], Izd. MGI, Moscow (1968).
68. L. V. Ershov, L. K. Liberman, and I. B. Neiman, Rock Mechanics [in Russian], Nedra, Moscow (1987).
69. A. Yu. Ishlinskii, "Stability of elastic bodies from the standpoint of the mathematical theory of elasticity," Ukr. Mat. Zh., 6, No. 2, 140-146 (1954).
70. G. G. Kuliev, Fracture and Stability of Three-Dimensional Cracked Bodies and Some Related Problems of Mining and Petroleum Rock Mechanics [in Russian], ÉLM, Baku (1983).
71. G. G. Kuliev and F. M. Asamidinov, "Stability of horizontal mine workings of circular cross section under biaxial compression," Prikl. Mekh., 13, No. 4, 122-124 (1977).
72. G. G. Kuliev and É. S. Makhmudov, "Stability analysis of the rock near vertical mine workings of arbitrary cross section," Izv. AN Azer. SSR, Ser. Fiz.-Tekhn. Mat. Nauk, 3, 27-31 (1980).
73. G. G. Kuliev and É. S. Makhmudov, "Elastic stability of the rock near a vertical mine working of elliptic cross section," Prikl. Mekh., 18, No. 6, 81-86 (1982).
74. G. G. Kuliev and É. S. Makhmudov, "Spatial elastic buckling mode of the rock near noncircular horizontal mine workings," Izv. AN SSSR, Mekh. Tverd. Tela, 6, 59-65 (1982).
75. Yu. V. Kokhanenko, "Numerical solution of the three-dimensional stability problem for a horizontal working of rectangular cross section (piecewise-homogeneous model)," Dokl. AN USSR, Ser. A, 2, 38-41, (1990).
76. L. S. Leibenzon, "Harmonic functions in the stability issue for spherical and cylindrical shells," in: Collected Papers [in Russian], Vol. 1, Izd. AN SSSR, Moscow (1951), pp. 50-83.
77. S. B. Lobovik, "Stability analysis of a spherical cavity by a variational method," Prikl. Mekh., 13, No. 2, 35-39 (1977).
78. S. B. Lobovik, "On stability of an incompressible half-space with a spherical cavity," Prikl. Mekh., 13, No. 12, 117-120 (1977).
79. É. S. Makhmudov, "Joint action of geostatic and geodynamic forces on the stability of the rock mass near a vertical mine working of circular cross section," Nauch. Tr. USKhA, 198, 153-154 (1978).
80. A. V. Navoyan, "On stability of a horizontal mine working under triaxial compression," Prikl. Mekh., 9, No. 6, 121-124 (1973).
81. A. V. Navoyan and A. N. Guz, "Formulation of and solution techniques for stability problems for horizontal mine workings," Dop. AN URSR, Ser. A, 3, 263-266 (1973).
82. V. M. Nazarenko, "On stability of mine workings in the presence of interfaces separating rocks with dissimilar physicomechanical properties," Dokl. AN USSR, Ser. A, 12, 34-38 (1980).
83. M. Nazarenko, "Stability of a horizontal mine working in rock mass with kinematic hardening," Prikl. Mekh., 17, No. 9, 124-127 (1981).
84. V. M. Nazarenko, "Stability of a horizontal mine working in the presence of interfaces separating rocks with dissimilar physicomechanical properties," Prikl. Mekh., 18, No. 6, 121-124 (1982).
85. V. M. Nazarenko, "Plane stability problem for horizontal mine workings in the presence of interfaces separating rocks with dissimilar physicomechanical properties," in: Proc. 9th Sci. Conf. Young Scient. Inst. Mech. Acad. Sci. Sov. Republ. Ukraine (Kiev, 1981) [in Russian], Kiev (1982), pp. 181-186.
86. V. M. Nazarenko, "Influence of a cracking region around a circular horizontal mine working on its stability," Prikl. Mekh., 20, No. 4, 136-137 (1984).
87. L. N. Nasonov, "Use of high-speed computers in solving problems of rock pressure in single drift-type mine workings," in: Analytical Methods for Study into and Mathematical Simulation of Rock Processes [in Russian], Gosgortekhizdat, Moscow (1963), pp. 43-45.
88. A. N. Sporykhin, "Stability of horizontal mine workings in elastoviscoplastic rock," Izv. AN Kaz. SSR, Ser. Fiz.-Mat. Nauk, 1, 67-72 (1975).
89. A. N. Sporykhin and A. N. Shashkin, "Stability of vertical mine workings in hardened plastic rock," Prikl. Mekh., 10, No. 11, 76-80 (1974).
90. M. A. Biot, Mechanics of Incremental Deformations, Willey, New York (1965).
91. L. V. Deriglazov, V. B. Medvedev, and N. N. Svirkov, "On the stability of bedrock in neighborhood of two horizontal excavations," J. Math. Sci., 74, No. 4 (1995).
92. A. N. Guz, "On the problems of stability of deformable systems under tracking loads," in: Theory of Shells, North-Holland, Amsterdam (1980), pp. 327-328.
93. A. N. Guz, "On the theory of stability of underground mine working," in: Mechanics of Jointed and Faulted Rock, A. A. Balkema, Rotterdam (1990), pp. 803-807.
94. A. N. Guz, "On three-dimensional linearized theory of stability of laminated rock (Continual theory and model of piecewise-homogeneous medium)," in: Mechanical Instability in Rocks and Tectonics. Abstracts, Montpellier, France (1991), pp. 18-19.
95. A. N. Guz, "Computational and variational methods in the theory of stability of underground mine workings (theory and results)," in: S. N. Atluri and G. Yagawa (eds.), Advances in Computational Engineering Science, Tech. Science Press, Forsyth, Georgia (1997), pp. 981-986.
96. A. N. Guz, "On the problems of computational and variational methods in the theory of stability of underground mine workings (theory and results)," in: Abstracts of Papers Read at ECCM'99 (August 31-September 3, 1999), Munich, Germany (1999), pp. 254-255.
97. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin (1999).
98. A. N. Guz, "Constructing the three-dimensional theory of stability of deformable bodies," Int. Appl. Mech., 37, No. 1, 1-37 (2001).
99. A. N. Guz and Yu. V. Kokhanenko, "Numerical solution of three-dimensional stability problems for elastic bodies," Int. Appl. Mech., 37, No. 11, 1369-1399 (2001).