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

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.