Generalized integral formulas based on the weight-function technique are used to calculate stress intensity and opening displacements for planar or axisymmetric fractures emanating from a cylindrical or spherical hole in an elastic medium. These approximate formulas reduce to known exact solutions in the limits of very short (notch) fractures or very long [penny-shaped or Griffith) fractures. In the intermediate range, where fracture length is comparable to hole size, the approximation is generally accurate within a few percent, as demonstrated by comparison with available numerical results for the planar problem of a circular hole with an arbitrary number of radial cracks as well as the axisymmetric problems of a cylindrical or spherical hole with a disk-shaped circumferential fracture. The generalized integral formulas provide a fast, simple, and reasonably accurate method for solving a broad class of engineering problems, including hydraulic and explosive fracturing applications, in which the following features are important: cavity pressurization, stress concentration around the cavity due to in situ compressive stresses, arbitrary pressure distribution along fracture, varying fracture length, and multiple fracturing.

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