Abstract
We investigate migration of fluids through the rock in the stress corrosion process. The fluids migrate along the trajectories of the principal stress field. We study geometry of these trajectories, including singularities, limit cycles, and possible bifurcations. We describe corresponding configurations of weakened zones in the lithosphere due to the fluid migration.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson, O. L., and Grew, P. C. (1977), Stress corrosion theory of crack propagation with application to geophysics, Rev. Geophys. Space Phys. 15, 7–104.
Andronov, A. A., Leontovich, E. A., Gordon, I. I., and Mayer, A. G., Qualitative Theory of Second Order Dynamic Systems (in Russian) ( Nauka, Moscow 1966 ).
Andronov, A. A., Leontovich, E. A., Gordon, I. I., and Mayer, A. G., Bifurcation Theory of Dynamic Systems on a Plane (in Russian) ( Nauka, Moscow 1967 ).
Barenblatt, G. I., and Christianovich, S. A. (1968), On the cohesion modulus in the theory of cracks (in Russian), Mech. Tverd. Tela 2, 70–75.
Barenblatt, G. I., Vishik, M. M., and Keilis -Borok, V. I. (1981), A model of clustering of earthquakes, Proc. Nat. Acad. Sci. U.S. 78, 5284–5287.
Cayley, A. (1863) On differential equations and umbilici, Philos. Mag. 26 ( Collected Works, Vol. V, paper 330 ).
Darboux, G., Lecons sur la Theorie Generale des Surfaces (Vol. 4 ) ( Gauthier-Villars, Paris 1896 ).
Frost, P. (1870), On the directions of lines of curvature in the neighborhood of an umbilicus, Q. J. Math. 10.
Gelfand, I. M., Guberman, SH. A., Keilis-Borok, V. I., et al. (1976), Pattern recognition applied to earthquake-prone areas in California, Phys. Earth. Planet. Internat. 11, 227–283.
Hallbauer, D. K., Wagner, H., and Cook, N. G. W. (1973), Some observations concerning the microscopic and mechanical behaviour of quartzite specimens in stiff triaxial compression tests, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 10, 713.
Kachanov, M. L. (1982), A microcrack model of rock inelasticity, Mech. Mater. 1, 19–42, 123–129.
Nemat-Nasser, S., and Horii, H. (1982), Compression induced non-planar crack extension with application to splitting, exfoliation and rockburst, J. Geophys. Res. 87, 6805–6821.
O’Neil, J. R., and Hanks, T. C. (1980), Geochemical evidence for interaction of water along the San Andreas fault in central California, J. Geophys. Res. 85, 6286.
Pertsov, N. V., and Kogan, B. S. (1981), Physicochemical geomechanics (in Russian), Physicochem. Mech. Lyophil. Dispers. Sys. 13, 53–64.
Pertsov, N. V., Kogan, B. S., and Balashov, V. N. (1977), Model of intrusion of magma into fractures in the presence of stress corrosion (in Russian), Dok. Akad. Nauk Ussr 235, 1375–1378.
Porteous, M. (1971), The normal singularities of a submanifold, J. Diff. Geom. 5, 543–564.
Rhebinder, P. A., and Shtchukin, E. D. (1972), Surface phenomena affecting solids in the process of deformation and fracturing (in Russian), Uspekh. Fiz. Nauk 108, 3–42.
Rice, J. R. (1979), Theory of precursory processes in the inception of earthquake rupture, Gerlands Beit. Geophys. 88, 91–127.
Sibson, R. H., Fluid flow accompanying faulting: field evidence and models, In Earthquake Prediction (Am. Geophys. Union, 1981 ) pp. 593–604.
Thom, R. (1955–56), Les singularités des applications différentiables, Ann. Inst. Fourier 6, 43–87.
Thom, R. (1969), Ensembles et morphismes stratifiés, Bull. Ams 75, 240–284.
Thorndike, A. S., C. R. Cooley, and J. F. Nye (1981), The structure and evolution offlow fields and other vector fields, J. of Physics, 11, 1455–1490.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer Basel AG
About this chapter
Cite this chapter
Gabrielov, A.M., Keilis-Borok, V.I. (1983). Patterns of Stress Corrosion: Geometry of the Principal Stresses. In: Knopoff, L., Keilis-Borok, V.I., Puppi, G. (eds) Instabilities in Continuous Media. Contributions to Current Research in Geophysics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6608-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-0348-6608-8_8
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-6609-5
Online ISBN: 978-3-0348-6608-8
eBook Packages: Springer Book Archive