Stability of a uniformly pressurized crack parallel to the surface of a semi-infinite elastic solid

Conference · Wed Dec 01 04:00:00 EST 1976 · EOS, Trans., Am. Geophys. Union; (United States)

OSTI ID:5401304

Holzhausen, G

Two methods have been used to model a pressurized crack parallel to the traction-free surface of a semi-infinite body in this study. One method treats the crack as a continuous distribution of dislocations and requires a numerical solution to a system of integral equations. The other method employs an iterative technique that superposes analytical solutions for a pressurized, flat crack in an infinite medium and for a semi-infinite body subjected to arbitrary surface loads to obtain an approximate solution to the given boundary value problem. Using these two methods stress intensities were calculated at crack tips as functions of crack depth to length ratios. These calculated stress intensities can be compared to experimentally determined critical stress intensities to predict the values of length, depth and pressure at which an hydraulic fracture will propagate unstably. The free surface begins to affect the crack tip stress intensity when the crack length is about equal to its depth. For crack depth to length ratios greater than one, stress intensity is adequately predicted by the model of a pressurized crack in an infinite body. When crack length is about four times the depth, the stress intensity at the crack tips increases markedly. At low depth to length ratios the plane of the crack begins to curve toward the free surface. The crack will eventually intersect the surface if propagation is allowed to continue. When the iterative technique is used, the number of iterations needed to converge on a solution increases as the crack depth to length ratio is reduced.

• Research Organization: Geological Survey, Menlo Park, CA
• OSTI ID: 5401304
• Conference Information: Journal Name: EOS, Trans., Am. Geophys. Union; (United States) Journal Volume: 57:12
• Country of Publication: United States
• Language: English

Related Subjects

58 GEOSCIENCES
580300* -- Mineralogy
Petrology
& Rock Mechanics-- (-1989)
CRACKS
EARTH CRUST
ELASTICITY
ITERATIVE METHODS
MATHEMATICAL MODELS
MECHANICAL PROPERTIES
SOLIDS
STABILITY
STRESSES
SURFACES
TENSILE PROPERTIES