HR: 16:45h
AN: V24B-04    [Abstracts]
TI: The Geometry of Shallow Sills and Hydraulic Fractures
AU: * Bunger, A P
EM: andrew.bunger@csiro.au
AF: CSIRO Petroleum Resources, Private Bag 10, Clayton South, Vic 3169 Australia
AU: Jeffrey, R G
EM: rob.jeffrey@csiro.au
AF: CSIRO Petroleum Resources, Private Bag 10, Clayton South, Vic 3169 Australia
AU: Detournay, E
EM: detou001@umn.edu
AF: University of Minnesota Department of Civil Engineering, 500 Pillsbury Drive, Minneapolis, MN 55455 United States
AB: We have studied in laboratory experiments the tendency of fluid-driven shallow subsurface fractures, such as magmatic sills or hydraulic fractures, to curve and form concave upward bowl-shaped structures. We consider the particular case of a crack driven by a Newtonian fluid that is: 1) initially radially-symmetric about the fluid-injection point and 2) initially parallel to the traction-free surface of a specimen subjected to a uniform normal compressive stress (σ_r) acting parallel to the free-surface. The results indicate that these fractures curve and the curving becomes strong when the radius is on the same order as the initial depth. The fractures eventually daylight, or erupt. The curving arises because of the mechanical/geometric asymmetry induced by the interaction of the fracture with the surface and in spite of the fact that the least compressive far-field stress direction is perpendicular to the surface.
The bowl-shaped fractures are not self-similar structures that scale by the initial depth, but rather the shape of the bowl is controlled by a dimensionless parameter which compares the magnitude of σ_r with a characteristic fracture-induced stress given by the fracture toughness (K_Ic) divided by the square-root of the initial depth (H). In particular, the larger the ratio σ_r √H/K_Ic, the flatter the bowl-shaped fracture will be and furthermore, two fractures will have approximately the same shape up to a re-scaling by H provided that the ratio σ_r √H/K_Ic is the same for the two cases. The bowl-shape is reasonably insensitive to the particulars of the internal pressure distribution, and therefore the geometric similarity dependence on σ_r √H/K_Ic suggests that its value at the time of fracture growth may be ascertained from the final fracture shape. It may also be concluded that propagation parallel to the surface corresponds to the limit of σ_r √H/K_Ic going to infinity.
These near-surface curving fractures do not always grow in a radially-symmetric manner. Rather, at some point, as the fracture grows larger, propagation favors a given direction to the detriment of the others resulting in a fracture that is egg-shaped in plan view. Hence, eruption at the surface occurs along only a small portion of the fracture's circumference (the pointed end of the egg) and the region of the fracture or sill immediately adjacent to the eruption point appears as a relatively short dike (compared with the fracture radius) with oblique to sub-horizontal intersection with the surface. Experimental results suggest that the circular-to-egg-shape transition occurs earlier in the fracture's life and results in more elongated egg-shapes when the relative importance of viscous dissipation, which may be quantified by a dimensionless ratio of the controlling parameters, takes on smaller values. Hence, the most elongated egg-shapes correspond to the uniform fluid pressure case that arises in the limit when viscous dissipation vanishes.
DE: 8414 Eruption mechanisms and flow emplacement
DE: 8434 Magma migration and fragmentation
DE: 8445 Experimental volcanism
SC: Volcanology, Geochemistry, Petrology [V]
MN: Fall Meeting 2005