Early-time solution for a radial hydraulic fracture

Andrew P. Bunger, Emmanuel Detournay

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


The small-time asymptotic solution for a penny-shaped fluid-driven fracture is obtained semianalytically. Scaling considerations indicate that the portion of the fracture that is filled with fluid increases with time according to a power law. The problem is shown to be self-similar at the length scale of the small fluid-filled region and to depend on only the mean fluid pressure at the length scale of the fracture. This similarity solution is unusual as the two length scales of the problem - the radius of the fracture and the radius of the fluid front - evolve according to two different power laws of time.

Original languageEnglish (US)
Pages (from-to)534-540
Number of pages7
JournalJournal of Engineering Mechanics
Issue number5
StatePublished - May 2007


  • Elasticity
  • Fracture
  • Hydraulics
  • Mechanics


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