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

被引：36
作者：
Bunger, AP
Detournay, E
机构：
[1] Univ Minnesota, Dept Civil Engn, Minneapolis, MN 55455 USA
[2] CSIRO Petr, Clayton 3169, Australia
来源：
ENGINEERING FRACTURE MECHANICS | 2005年 / 72卷 / 16期
关键词：
hydraulic fracture; blister crack; fracture mechanics; matched asymptotics; free-surface effects;
D O I：
10.1016/j.engfracmech.2005.03.005
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
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. (c) 2005 Elsevier Ltd. All rights reserved.
引用
收藏
页码：2468 / 2486
页数：19
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