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

  • John R. Lister (a1)

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.

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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, 259287.
Anderson, O. L. 1978 The role of magma vapours in volcanic tremors and rapid eruptions. Bull. Volcanol. 41, 341353.
Anderson, O. L. & Grew, P. C. 1977 Stress corrosion theory of crack propagation with applications to geophysics. Rev. Geophys. Space Phys. 15, 77103.
Atkinson, B. K. 1984 Subcritical crack growth in geological materials. J. Geophys. Res. 89, 40774114.
Barenblatt, G. I. 1962 The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7, 55129.
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, 373431.
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, 1248.
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, 39104.
Huppert, H. E., Sparks, R. S. J., Turner, J. S. & Arndt, N. T. 1984 Emplacement and cooling of komatiite lavas. Nature 309, 1922.
Irwin, G. R. 1958 Fracture. In Handbuch der Physik VI (ed. S. Flügge), pp. 551590. Springer.
Lister, J. R. 1989 Fluid-mechanical models of crack propagation and their application to magma-transport in dykes. Geophys. Res. Lett. (in preparation).
Maaloe, S. 1987 The generation and shape of feeder dykes from mantle sources. Contr. Min. Petrol. 96, 4755.
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, 559583.
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, 2757.
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, 975984.
Reches, Z. & Fink, J. 1988 The mechanism of intrusion of the Inyo Dike, Long Valley Caldera, California. J. Geophys. Res. 93, 43214334.
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. 201264. Princeton.
Spence, D. A. & Sharp, P. W. 1985 Self-similar solutions for elastohydrodynamic cavity flow.. Proc. R. Soc. Lond. A 400, 289313.
Spence, D. A., Sharp, P. W. & Turcotte, D. L. 1987 Buoyancy-driven crack propagation: a mechanism for magma migration. J. Fluid Mech. 174, 135153 (referred to as SST).
Spera, F. 1980 Aspects of magma transport. In Physics of Magmatic Processes (ed. R. B. Hargreaves), pp. 265323. Princeton.
Weertman, J. 1971 The theory of water-filled crevasses in glaciers applied to vertical magma transport beneath oceanic ridges. J. Geophys. Res. 76, 11711183.
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