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

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 similar to s(3/2) (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 similar to s(2/3) 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 similar to s(1/3) 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. (C) 2017 Elsevier Ltd. All rights reserved.