Asymptotic solution for a penny-shaped near-surface hydraulic fracture

Andrew P. Bunger, Emmanuel Detournay

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


This paper considers the large time asymptotic behavior of a near-surface hydraulic fracture, that is, when the radius (R) is much larger than the depth (H). The fracture is analyzed as an elastically clamped circular plate and stress intensity factors are determined by matching the outer plate problem to the inner problem of a near-surface semi-infinite crack. In the zero-viscosity limit, we derive two terms of a large R/H asymptotic solution. Comparison shows that the accuracy of some published numerical results deteriorates for R/H > 5. This is corrected using smaller element size to ensure that the crack-tip element is entirely in the region that is well-approximated by a square-root tip asymptote.

Original languageEnglish (US)
Pages (from-to)2468-2486
Number of pages19
JournalEngineering Fracture Mechanics
Issue number16
StatePublished - Nov 2005

Bibliographical note

Funding Information:
The authors wish to acknowledge support from the Australian Coal Association Research Program (ACARP) and the CSIRO Division of Petroleum Resources. We thank Dr. Xi Zhang for contributing the corrected numerical results (“Refined ZDJ”) and Dr. Rob Jeffrey for his helpful discussion of this problem.


  • Blister crack
  • Fracture mechanics
  • Free-surface effects
  • Hydraulic fracture
  • Matched asymptotics


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