Problems of folding in the earth's stratified crust

International Applied Mechanics

Volumn 43, Issue 2, 2007, Pages 127-159

  Guz, A N ^a   Chekhov, V N ^a  

^a S P TIMOSHENKO INSTITUTE OF MECHANICS   (Ukraine)

Author keywords

Earth's stratified crust; Folded structure; Folding; Piecewise homogeneous medium model; Three dimensional theory of stability

Indexed keywords

EARTH'S STRATIFIED CRUST; FOLDED STRUCTURE; FOLDING; PIECEWISE HOMOGENEOUS MEDIUM MODEL; THREE DIMENSIONAL THEORY OF STABILITY;

EARTH (PLANET); MATHEMATICAL MODELS; MECHANICAL PROPERTIES; PROBLEM SOLVING; THREE DIMENSIONAL;

SURFACE ANALYSIS;

EID: 34547498387     PISSN: 10637095     EISSN: 15738582     Source Type: Journal    
DOI: 10.1007/s10778-007-0013-y     Document Type: Article

References (90)

1. V. V. Belousov, Basic Issues of Geotectonics [in Russian], Gostekhizdat, Moscow (1962).
2. A. F. Bulat and V. N. Chekhov, "Problems of stability of the wall rock in the working of deep coal seams," Int. Appl. Mech., 28, No. 12, 832-838 (1992).
3. A. F. Bulat and V. N. Chekhov, "Three-dimensional problems of wall-rock stability in the vicinity of a cleaned working with control exercised over the stress-strain state of the mass," Int. Appl. Mech., 30, No. 8, 593-598 (1994).
4. A. N. Guz, Stability of Three-Dimensional Deformable Bodies [in Russian], Naukova Dumka, Kyiv (1971).
5. A. N. Guz, "On stability problems in rock mechanics," in: Problems of Rock Mechanics [in Russian], Nauka, Alma-Ata (1972), pp. 27-35.
6. A. N. Guz, Stability of Elastic Bodies under Finite Strains [in Russian], Naukova Dumka, Kyiv (1973).
7. A. N. Guz, "Determination of follower loads in the case of small strains," Dokl. AN USSR, Ser. A, No. 10, 908-912 (1976).
8. A. N. Guz, Fundamentals of the Theory of Stability of Mine Workings [in Russian], Naukova Dumka, Kyiv (1977).
9. A. N. Guz, "Sufficient applicability conditions for the Euler method in the case of a follower load acting on a part of the surface of a body," Dokl. AN USSR, Ser. A, No. 10, 901-905 (1977).
10. A. N. Guz, Stability of Elastic Bodies under Triaxial Compression [in Russian], Naukova Dumka, Kyiv (1979).
11. A. N. Guz, "Variational principles in the three-dimensional theory of stability of deformable bodies under follower loads," Dokl. AN SSSR, 246, No. 6, 1314-1316 (1979).
12. A. N. Guz, "Three-dimensional stability theory of deformable bodies: Surface instability," Int. Appl. Mech., 22, No. 1, 17-26 (1986).
13. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies [in Russian], Vyshcha Shkola, Kyiv (1986).
14. A. N. Guz, Fracture Mechanics of Compressed Composite Materials [in Russian], Naukova Dumka, Kyiv (1990).
15. A. N. Guz, "Constructing the three-dimensional theory of stability of deformable bodies," Int. Appl. Mech., 37, No. 1, 1-37 (2001).
16. A. N. Guz, "Establishing the fundamentals of the theory of stability of mine workings," Int. Appl. Mech., 39, No. 1, 20-46 (2003).
17. A. N. Guz, V. P. Korzh, and V. N. Chekhov, "Stability of a layered half-plane under distributed surface loads," Dokl. AN SSSR, 313, No. 6, 1381-1384 (1990).
18. A. N. Guz, E. A. Tkachenko, V. N. Chekhov, and V. S. Stukotilov, "Surface bulging of multilayer coatings with regular structure," Dokl. NAN Ukrainy, No. 9, 66-70 (1996).
19. A. N. Guz and V. N. Chekhov, "Application of the linearized stability equations to study folding in the Earth's crust," in: Abstracts of the 5th Kazakh. Interuniv. Conf. [in Russian], 4.2, Nauka, Alma-Ata (1974), pp. 64-65.
20. A. N. Guz and V. N. Chekhov, "Linearized theory of folding in the interior of the earth's crust, " Int. Appl. Mech., 11, No. 1, 3-10 (1975).
21. A. N. Guz and V. N. Chekhov, "Surface instability of a layered half-plane with elastoplastic layers, " Dokl. AN SSSR, 272, No. 3, 546-550 (1983).
22. A. N. Guz and V. N. Chekhov, "Application of variational methods in stability problems for semibounded layered media," Dokl. AN SSSR, 283, No. 5, 1120-1124 (1985).
23. A. N. Guz and V. N. Chekhov, "Investigation of surface instability of stratified bodies in a three-dimensional formulation," Int. Appl. Mech., 26, No. 2, 107-125 (1990).
24. A. N. Guz, V. N. Chekhov, and N. A. Shul'ga, "Surface instability of a layered half-space with periodic structure," Dokl. AN SSSR, 266, No. 6, 1306-1310 (1982).
25. A. K. Egorov, "On incipient folding in a stack of layers," Izv. AN KazSSR, Ser. Fiz.-Mat., No. 1, 22-27 (1966).
26. Zh. S. Erzhanov and A. K. Egorov, Theory of Folding in Rock Mass (Mathematical Description) [in Russian], Nauka, Alma-Ata, (1968).
27. Zh. S. Erzhanov, A. K. Egorov, I. A. Garagash, et al., Theory of Folding in the Earth's Crust [in Russian], Nauka, Moscow (1974).
28. Zh. S. Erzhanov and A. K. Egorov, Stability of Inhomogeneous Deformation of Nonlinear Bodies [in Russian], Nauka, Alma-Ata (1987).
29. V. E. Zabigailo, A. Z. Shirokov, and V. V. Lukinov, Geological Factors of Outburst Hazard in Donbass [in Russian], Naukova Dumka, Kyiv (1974).
30. A. N. Zorin, Yu. M. Khalimendik, and V. G. Kolesnik, Fracture Mechanics of Rock Mass and Use of Its Energy in Mining [in Russian], Nedra, Moscow (2001).
31. Yu. A. Kosygin, Tectonics [in Russian], Nedra, Moscow (1964).
32. A. Ya. Radzivill, "Tectonophysical features of Tovtry ridge structures," Dop. AN URSR, Ser. B, 504-506 (1975).
33. A. Ya. Radzivill, "Role of extensional and compressional structures of different ranks in the redistribution of substance and energy in the tectonosphere and in the formation of mineral deposits," Nauk. Pratsi Inst. Fund. Doslidzh., 9, 11-20 (1995).
34. A. Ya. Radzivill, Carbon-Bearing Formations and Orogenic Structures of Ukraine [in Russian], Naukova Dumka, Kyiv (1994).
35. B. M. Usachenko, Properties of Rocks and Stability of Mine Workings [in Russian], Naukova Dumka, Kyiv (1979).
36. A. I. Cherednichenko, Tectonophysical Conditions for Mineral Transformations [in Russian], Naukova Dumka, Kyiv (1964).
37. V. N. Chekhov, "Effect of a follower load on the fold formation in the Earth's crust," Int. Appl. Mech., 11, No. 5, 528-532 (1975).
38. V. N. Chekhov, "Analysis of fold formation in the earth's crust on the basis of the stability equation for thin plates," Int. Appl. Mech., 11, No. 8, 899-902 (1975).
39. V. N. Chekhov, "Analysis of fold formation in the earth's crust during inelastic deformation of layers," Int. Appl. Mech., 11, No. 11, 1229-1232 (1975).
40. V. N. Chekhov, "Investigation of folding process in nonlinear subcritical state," Int. Appl. Mech., 12, No. 4, 351-367 (1976).
41. V. N. Chekhov, "Dynamic approach to problems of fold formation in the earth's crust," Int. Appl. Mech., 12, No. 7, 712-715 (1976).
42. V. N. Chekhov, "Postcritical behavior of folds in rock strata in the Earth's crust," in: New Results of Geophysical Survey in Ukraine [in Russian], Naukova Dumka, Kyiv (1977), pp. 48-54.
43. V. N. Chekhov, "Folding of rock layers under tracking surface loads," Int. Appl. Mech., 18, No. 7, 606-611 (1982).
44. V. N. Chekhov, "A note on folding in rock strata," in: Mathematical Modeling of Geophysical Fields [in Russian], Naukova Dumka, Kyiv (1982), pp. 12-18.
45. V. N. Chekhov, "Folding of rocks with periodic structure," Int. Appl. Mech., 20, No. 3, 216-222 (1984).
46. V. N. Chekhov, "Effect of the hereditary properties of a medium on the surface instability of a layered half-space," Int. Appl. Mech., 20, No. 7, 613-619 (1984).
47. V. N. Chekhov, "Surface instability of a layered medium connected to a uniform half-space," Int. Appl. Mech., 20, No. 11, 1018-1025 (1984).
48. V. N. Chekhov, "Influence of surface load on stability of laminar bodies," Int. Appl. Mech., 24, No. 9, 839-845 (1988).
49. V. N. Chekhov, "Structural instability of regularly layered semibounded bodies," Prikl. Mekh., 24, No. 11, 110-112 (1988).
50. V. N. Chekhov, "Formulation of problems in the three-dimensional linearized theory of folding," in: Proc. of Ukrainian-Polish Forum of Miners [in Russian], Donetsk (2004), pp. 521-532.
51. V. N. Chekhov, "Allowance for the viscoelastic properties of rocks in problems of folding in the Earth's stratified crust," in: Proc. Int. Sci.-Tech., Symp. on Geoinformation Monitoring of the Environment (September 6-11, 2004) [in Ukrainian], Lviv (2004), pp. 18-19.
52. V. M. Chekhov, "Establishing conditions for the formation of folded structures in a stratified rock mass near the surface," in: Proc. 2nd Sci.-Tech. Conf. on Today's Hazardous Geological Processes: Forecasting and Protection (Alushta, the Crimea, September 27-October 1, 2004) [in Ukrainian], Znannya, Kyiv (2004), pp. 52-53.
53. V. N. Chekhov, "Influence of the elastic characteristics of rocks on linear folding in the Earth's crust," Geoinformatika, No. 4, 71-76 (2005).
54. V. N. Chekhov and É. A. Tkachenko, "Stability of a laminate between two homogeneous half-spaces under inelastic deformation," Int. Appl. Mech., 42, No. 5, 481-489 (2005).
55. V. M. Chekhov, V. D. Omel'chenko, and É. A. Tkachenko, "Study of folding in a stratified rock mass based on mantle sounding data," Nauk. Visn. NGAU, No. 4, 117-120 (2001).
56. V. M. Chekhov, V. D. Omel'chenko, and É. A. Tkachenko, "Determining the mechanical properties of rocks and studying folding in the Earth's stratified crust," Visn. Kyiv. Univ., Geologiya, 23-24, 23-25 (2002).
57. N. A. Shul'ga, Fundamentals of the Mechanics of Layered Media with Periodic Structure [in Russian], Naukova Dumka, Kyiv (1981).
58. V. E. Khain, General Geotectonics [in Russian], Nedra, Moscow (1973).
59. O. V. Kharitonov and V. D. Omel'chenko, "Deep structure and dynamics of the Earth's crust across the Kremenchug-Putivl profile," Dokl. NAN Ukrainy, No. 2, 101-108 (1996).
60. S. D. Akbarov and A. N. Guz, Mechanics of Curved Composites, Kluwer Academic Publishers, Dordreht-Boston-London (2000).
61. M. A. Biot, "Folding instability of a layered viscoelastic medium under compression," Proc. Roy. Soc., Ser. A, 242, 12-31 (1957).
62. M. A. Biot, "Folding of a layered viscoelastic medium derived from an exact stability theory of a continuum under initial stress," Quart. Appl. Math., 17, No. 2, 186-204 (1959).
63. M. A. Biot, "The influence of gravity on the folding of a layered viscoelastic medium under compression," J. Franklin Inst., 267, No. 3, 211-228 (1959).
64. M. A. Biot, "On the instability and folding deformation of a layered viscoelastic medium in compression," Trans ASME, J. Appl. Mech., 26, No. 3, 393-400 (1959).
65. M. A. Biot, "Theory of folding of stratified viscoelastic media and its implication in tectonics and orogenesis," Bull. Geol. Soc. Amer., 72, 1595-1620 (1961).
66. M. A. Biot, "Surface instability in finite anisotropic elasticity under initial stress," Proc. Roy. Soc., Ser. A, 273, 329-339 (1963).
67. M. A. Biot, "Interfacial instability in finite elasticity under initial stress," Proc. Roy. Soc., Ser. A, 273, 340-344 (1963).
68. M. A. Biot, "Theory of stability of multilayered continua in finite anisotropic elasticity," J. Francklin Inst., 276, No. 2, 128-153 (1963).
69. M. A. Biot, Mechanics of Incremental Deformanions, Wiley & Sons, New York (1965).
70. M. A. Biot, H. Ode, and W. L. Roever, "Experimental verification of the theory of folding of stratified viscoelastic media," Bull. Geol. Soc. Amer., 72, No. 11, 1621-1632 (1961).
71. P. Blay, J. W. Cosgrrove, and J. M. Summers, "An experimental investigation of the development of structures in multilayers under the influence of gravity," J. Geol. Soc. London, 133, No. 4, 329-342 (1977).
72. A. F. Bulat, "Current challenges of geotechnical mechanics," Int. Appl. Mech., 42, No. 9, 967-975 (2006).
73. V. N. Chekhov, "On the formation of linear folds in regularly layered rock masses under biaxial loading," Int. Appl. Mech., 41, No. 12, 1350-1356 (2005).
74. R. Edmunds, G. W. Hunt, and M. A. Wadee, "Parallel folding in multilayered structures," J. Mech. Phys. Solids, 54, 384-400 (2006).
75. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin (1999).
76. A. N. Guz, "Design models in linearized solid mechanics," Int. Appl. Mech., 40, No. 5, 506-516 (2004).
77. A. N. Guz and V. N. Chekhov, "On the determination of loads upon the ground support in underground mine workings," Int. Appl. Mech., 41, No. 11, 1239-1245 (2005).
78. I. A. Guz, "3D comparative analysis of different buckling modes in layered rocks," in: Proc 9th Int. Conf. on the Mechanical Behavior of Materials (ICM9) (May 25-29, 2003), Geneva, Switzerland (2003), pp. 125-131.
79. I. Guz and C. Soutis, "On application of the continuum fracture theory to layered rocks," in: Abstracts of Eur. Conf. on Computational Mechanics (August 31-September 3, 1999), Munich, Germany (1999), pp. 252-253.
80. P. H. Kuenen and L. U. de Sitter, "Experimental investigation into the mechanism of folding," Leidche Geol. Med., 12, 219-239 (1938).
81. Y. Maystrenko, V. D. Omelchenko, R. Stephenson, et al., "Crustal-scale pop-up structure in cratonic lithosphere: DOBRE deep seismic reflection study of the Donbas Foldbelt, Ukraine," Geology, 31, No. 8, 733-736 (2003).
82. J. G. Ramsey, Folding and Fracturing of Rocks, McGraw-Hill, New York (1967).
83. H. Ramberg, "Contact strain and folding instability of a multilayered body under compression," Geol. Rundschau, 51, 465-439 (1962).
84. H. Ramberg, "Fluid dynamics of viscous buckling applicable to folding of layered rocks," Bull. Amer. Assoc. Petrol. Geologists, 47, No. 3, 22-31 (1963).
85. N. J. Price and J. W. Cosgrove, Analysis of Geological Structures, Cambridge University Press, Cambridge (1990).
86. I. Peterson, "Axially loaded column subjected to lateral pressure," AIAA J., 1, No. 6, 1458-1459 (1981).
87. L. U. Sitter, Structural Geology, McGraw-Hill, New York (1956).
88. V. S. Stukotilov and V. N. Chekhov, "Surface instability of orthotropic laminated materials under compression," Int. Appl. Mech., 42, No. 7, 782-789 (2006).
89. M. Smoluchowski, "Einige Bemerkungen über die physikalschen Grundland der Theorien der Gebirgsbildung," Kosmos (Lwow), 34 (1909).
90. M. Smoluchowski, Versuche über Faltungserscheinungen Shwimmender elastischer Platten, Akademie der Wissenschaften, Mathematishe KIasse, Krakau (1910).