Effective-medium theory for the fracture of fractal porous media

A general energy-balance theory is developed for the fracture of fractal porous media using an effective-medium approximation to couple the fracture resistance to the (fractal) mass distribution. The decreasing resistance field derived increases the size and rate of size increase of flaws under the influence of localized loading. A general destabilizing field associated with a uniform applied stress is presented and used to examine the strength behavior: Strength is predicted to scale with the dominant flaw size according to 0c0(D-3-a)2, where D is the fractal dimension of the medium (<3), and a is an exponent characterizing the variation of the destabilizing field with crack length (>1). Hence, for a given distribution of flaw sizes, a porous fractal medium will exhibit lower, more variable strengths than a homogeneous medium. © 1989 The American Physical Society.