Similarity solutions for a shallow hydraulic fracture

Emmanuel Detournay, Andrew P. Bunger

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

This paper deals with the plane strain problem of a "shallow" fluid-driven fracture propagating parallel to a free-surface in an impermeable elastic rock. This problem has applications into magma-driven fractures such as sills, conditioning of ore masses by hydraulic fracturing to enhance caveability, and excavation of hard rocks by hydraulic means. We present two similarity solutions for cases when the fracture length is large compared to its depth: (i) the Ō solution with only a small fraction of the fracture occupied by the injected fluid, and (ii) the K̄ solution with the fracture completely filled by the fluid. It is shown that the Ō solution captures an intermediate episode of the fracture propagation under conditions of "small" toughness and confining stress and that the K̄ solution corresponds to the large time asymptotic evolution of the fracture.

Original languageEnglish (US)
Title of host publicationProceedings of the International Symposium of the International Society for Rock Mechanics, Eurock 2006 - Eurock 2006 Multiphysics Coupling and Long Term Behaviour in Rock Mechanics
Pages57-62
Number of pages6
StatePublished - Dec 1 2006
EventInternational Symposium of the International Society for Rock Mechanics, Eurock 2006 - Eurock 2006 Multiphysics Coupling and Long Term Behaviour in Rock Mechanics - Liege, Belgium
Duration: May 9 2006May 12 2006

Publication series

NameProceedings of the International Symposium of the International Society for Rock Mechanics, Eurock 2006 - Eurock 2006 Multiphysics Coupling and Long Term Behaviour in Rock Mechanics

Other

OtherInternational Symposium of the International Society for Rock Mechanics, Eurock 2006 - Eurock 2006 Multiphysics Coupling and Long Term Behaviour in Rock Mechanics
CountryBelgium
CityLiege
Period5/9/065/12/06

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    Detournay, E., & Bunger, A. P. (2006). Similarity solutions for a shallow hydraulic fracture. In Proceedings of the International Symposium of the International Society for Rock Mechanics, Eurock 2006 - Eurock 2006 Multiphysics Coupling and Long Term Behaviour in Rock Mechanics (pp. 57-62). (Proceedings of the International Symposium of the International Society for Rock Mechanics, Eurock 2006 - Eurock 2006 Multiphysics Coupling and Long Term Behaviour in Rock Mechanics).