Laboratory measurement of tip and global behavior for zero - toughness hydraulic fractures with circular and blade-shaped (PKN) geometry
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In: Journal of the mechanics and physics of solids, Vol. 104.2017, No. July, 21.04.2017, p. 172-186.
Research output: Contribution to journal › Article › Research › peer-review
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TY - JOUR
T1 - Laboratory measurement of tip and global behavior for zero - toughness hydraulic fractures with circular and blade-shaped (PKN) geometry
AU - Xing, Pengju
AU - Yoshioka, Keita
AU - Adachi, Jose
AU - El-Fayoumi, Amr
AU - Bunger, Andrew P.
PY - 2017/4/21
Y1 - 2017/4/21
N2 - 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.
AB - 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.
KW - Fluid-driven fractures
KW - Hydraulic fracturing
KW - Asymptotic analysis
U2 - 10.1016/j.jmps.2017.04.013
DO - 10.1016/j.jmps.2017.04.013
M3 - Article
VL - 104.2017
SP - 172
EP - 186
JO - Journal of the mechanics and physics of solids
JF - Journal of the mechanics and physics of solids
SN - 0022-5096
IS - July
ER -