Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-18T05:39:50.741Z Has data issue: false hasContentIssue false
  • English
  • Français

Buoyancy-driven fluid fracture: the effects of material toughness and of low-viscosity precursors

Published online by Cambridge University Press:  26 April 2006

John R. Lister
John R. Lister
Affiliation:
Research School of Earth Sciences, Australian National University, PO Box 4, Canberra 2601, ACT, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

When buoyant fluid is released into the base of a crack in an elastic medjura the crack will propagate upwards, driven by the buoyancy of the fluid. Viscous fluid flow in such a fissure is described by the equations of lubrication theory with the pressure given by the sum of the hydrostatic pressure of the fluid and the elastic pressures exerted by the walls of the crack. The elastic pressure and the width of the crack are further coupled by an integro-differential equation derived from the theory of infinitesimal dislocations in an elastic medium. The steady buoyancy-driven propagation of a two-dimensional fluid-filled crack through an elastic medium is analysed and the governing equations for the pressure distribution and the shape of the crack are solved numerically using a collocation technique. The fluid pressure in the tip of an opening crack is shown to be very low. Accordingly, a region of relatively inviscid vapour or exsolved volatiles in the crack tip is predicted and allowed for in the formulation of the problem. The solutions show that the asymptotic width of the crack, its rate of ascent and the general features of the flow are determined primarily by the fluid mechanics; the strength of the medium and the vapour pressure in the crack tip affect only the local structure near the advancing tip of the crack. When applied to the transport of molten rock through the Earth's lithosphere by magma-fracture, this conclusion is of fundamental importance and challenges the geophysicist's usual emphasis on the controlling influence of fracture mechanics rather than that of fluid mechanics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 210 , January 1990 , pp. 263 - 280
Copyright
© 1990 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aki, K., Fehler, M. & Das, S. 1977 Source mechanisms of volcanic tremor: fluid-driven crack models and their application to the 1963 Kilauea eruption. J. Volcanol. Geotherm. Res. 2, 259–287.Google Scholar
Anderson, O. L. 1978 The role of magma vapours in volcanic tremors and rapid eruptions. Bull. Volcanol. 41, 341–353.Google Scholar
Anderson, O. L. & Grew, P. C. 1977 Stress corrosion theory of crack propagation with applications to geophysics. Rev. Geophys. Space Phys. 15, 77–103.Google Scholar
Atkinson, B. K. 1984 Subcritical crack growth in geological materials. J. Geophys. Res. 89, 4077–4114.Google Scholar
Barenblatt, G. I. 1962 The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7, 55–129.Google Scholar
Bruce, P. M. & Huppert, H. E. 1989 Solidification and melting in dykes by the laminar flow of basaltic magma. In Magma Transport and Storage (ed. M. P. Ryan). Wiley.
Carmichael, I. S. E., Nicholls, J., Spera, F. J., Wood, B. J. & Nelson, S. A. 1977 High temperature properties of silicate liquids: applications to the equilibration and ascent of basic magma.. Phil. Trans. R. Soc. Lond. A 286, 373–431.Google Scholar
Carslaw, H. S. 1930 Introduction to the Theory of Fourier's Series and Integrals. Dover.
Dziewonski, A. M., Hales, A. L. & Lapwood, E. R. 1975 Parametrically simple Earth models consistent with geophysical data. Phys. Earth Planet. Inter. 10, 12–48.Google Scholar
Erdelyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. (eds.) 1954 Tables of Integral Transforms. McGraw Hill.
Griggs, D. T., Turner, F. J. & Heard, H. C. 1960 Deformation of rocks at 500°C to 800°C. In Rock Deformation. Geol. Soc. Am. Mem. 79, 39–104.Google Scholar
Huppert, H. E., Sparks, R. S. J., Turner, J. S. & Arndt, N. T. 1984 Emplacement and cooling of komatiite lavas. Nature 309, 19–22.Google Scholar
Irwin, G. R. 1958 Fracture. In Handbuch der Physik VI (ed. S. Flügge), pp. 551–590. Springer.
Lister, J. R. 1989 Fluid-mechanical models of crack propagation and their application to magma-transport in dykes. Geophys. Res. Lett. (in preparation).Google Scholar
Maaloe, S. 1987 The generation and shape of feeder dykes from mantle sources. Contr. Min. Petrol. 96, 47–55.Google Scholar
Macdonald, R., Wilson, L., Thorpe, R. S. & Martin, A. 1988 Emplacement of the Cleveland Dyke: evidence from geochemistry, mineralogy and physical modelling. J. Petrol. 29, 559–583.CrossRefGoogle Scholar
Pollard, D. D. 1988 Elementary fracture mechanics applied to the structural interpretation of dykes. In Mafic Dyke Swarms (eds. H. C. Halls & W. H. Fahrig). Geol. Soc. Canada Special Paper 33.
Pollard, D. D. & Holzhausen, G. 1979 On the mechanical interaction between a fluid-filled fracture and the Earth's surface. Tectonophysics 53, 27–57.Google Scholar
Pollard, D. D. & Muller, O. H. 1976 The effects of gradients in regional stress and magma pressure on the form of sheet intrusions in cross-section. J. Geophys. Res. 91, 975–984.Google Scholar
Reches, Z. & Fink, J. 1988 The mechanism of intrusion of the Inyo Dike, Long Valley Caldera, California. J. Geophys. Res. 93, 4321–4334.Google Scholar
Rubin, A. M. & Pollard, D. D. 1987 Origins of blade-like dikes in volcanic rift zones. US Geol. Surv. Professional Paper 1350.
Shaw, H. R. 1980 The fracture mechanisms of magma transport from the mantle to the surface. In Physics of Magmatic Processes (ed. R. B. Hargreaves), pp. 201–264. Princeton.
Spence, D. A. & Sharp, P. W. 1985 Self-similar solutions for elastohydrodynamic cavity flow.. Proc. R. Soc. Lond. A 400, 289–313.Google Scholar
Spence, D. A., Sharp, P. W. & Turcotte, D. L. 1987 Buoyancy-driven crack propagation: a mechanism for magma migration. J. Fluid Mech. 174, 135–153 (referred to as SST).Google Scholar
Spera, F. 1980 Aspects of magma transport. In Physics of Magmatic Processes (ed. R. B. Hargreaves), pp. 265–323. Princeton.
Weertman, J. 1971 The theory of water-filled crevasses in glaciers applied to vertical magma transport beneath oceanic ridges. J. Geophys. Res. 76, 1171–1183.Google Scholar