×

zbMATH — the first resource for mathematics

Propagation of a penny-shaped fluid-driven fracture in an impermeable rock: Asymptotic solutions. (English) Zbl 1032.74640
Summary: This paper presents an analysis of the propagation of a penny-shaped hydraulic fracture in an impermeable elastic rock. The fracture is driven by an incompressible Newtonian fluid injected from a source at the center of the fracture. The fluid flow is modeled according to lubrication theory, while the elastic response is governed by a singular integral equation relating the crack opening and the fluid pressure. It is shown that the scaled equations contain only one parameter, a dimensionless toughness, which controls the regimes of fracture propagation. Asymptotic solutions for zero and large dimensionless toughness are constructed. Finally, the regimes of fracture propagation are analyzed by matching the asymptotic solutions with results of a numerical algorithm applicable to arbitrary toughness.

MSC:
74R10 Brittle fracture
74L10 Soil and rock mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI