Laboratory measurement of tip and global behavior for zero - toughness hydraulic fractures with circular and blade-shaped (PKN) geometry

Pengju Xing, Keita Yoshioka, Jose Adachi, Amr El-Fayoumi, Andrew P. Bunger

Research output: Contribution to journalArticleResearchpeer-review


The tip behavior of hydraulic fractures is characterized by a rich nesting of asymptotic solutions, comprising a formidable challenge for the development of efficient and accurate numerical simulators. We present experimental validation of several theoretically-predicted asymptotic behaviors, namely for hydraulic fracture growth under conditions of negligible fracture toughness, with growth progressing from early-time radial geometry to large-time blade-like (PKN) geometry. Our experimental results demonstrate: 1) existence of a asymptotic solution of the form w ∼ s3/2 (LEFM) in the near tip region, where w is the crack opening and s is the distance from the crack tip, 2) transition to an asymptotic solution of the form w ∼ s2/3 away from the near-tip region, with the transition length scale also consistent with theory, 3) transition to an asymptotic solution of the form w ∼ s1/3 after the fracture attains blade-like (PKN) geometry, and 4) existence of a region near the tip of a blade-like (PKN) hydraulic fracture in which plane strain conditions persist, with the thickness of this region of the same order as the crack height.
Original languageEnglish
Pages (from-to)172-186
Number of pages7
JournalJournal of the mechanics and physics of solids
Issue numberJuly
Publication statusE-pub ahead of print - 21 Apr 2017
Externally publishedYes


  • Fluid-driven fractures
  • Hydraulic fracturing
  • Asymptotic analysis

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