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

• Published in: Journal of the mechanics and physics of solids Vol. 104; pp. 172 - 186
• Main Authors: Xing, Pengju, Yoshioka, Keita, Adachi, Jose, El-Fayoumi, Amr, Bunger, Andrew P.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 01.07.2017; Elsevier BV
• Subjects: Asymptotic analysis; Asymptotic properties; Computer simulation; Crack propagation; Fluid-driven fractures; Fracture mechanics; Fracture toughness; Hydraulic fracturing; Nesting; Numerical prediction; Plane strain; Simulators; Strain; Studies; Asymptotic analysis; Hydraulic fracturing; Fluid-driven fractures
• ISSN: 0022-5096; 1873-4782
• DOI: 10.1016/j.jmps.2017.04.013

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.