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

Andrew P. Bunger; Emmanuel Detournay

doi:10.1016/j.engfracmech.2005.03.005

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

Andrew P. Bunger, Emmanuel Detournay

Civil, Environmental, and Geo- Engineering

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	2468-2486
Number of pages	19
Journal	Engineering Fracture Mechanics
Volume	72
Issue number	16
DOIs	https://doi.org/10.1016/j.engfracmech.2005.03.005
State	Published - 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.

Keywords

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

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10.1016/j.engfracmech.2005.03.005

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title = "Asymptotic solution for a penny-shaped near-surface hydraulic fracture",

abstract = "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.",

keywords = "Blister crack, Fracture mechanics, Free-surface effects, Hydraulic fracture, Matched asymptotics",

author = "Bunger, {Andrew P.} and Emmanuel Detournay",

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. ",

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AU - Bunger, Andrew P.

AU - Detournay, Emmanuel

N1 - 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.

PY - 2005/11

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N2 - 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.

AB - 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.

KW - Blister crack

KW - Fracture mechanics

KW - Free-surface effects

KW - Hydraulic fracture

KW - Matched asymptotics

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DO - 10.1016/j.engfracmech.2005.03.005

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SN - 0013-7944

VL - 72

SP - 2468

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JO - Engineering Fracture Mechanics

JF - Engineering Fracture Mechanics

IS - 16

ER -

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

Abstract

Bibliographical note

Keywords

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