The mechanics of cracks and a statistical strength theory for rocks

Features of the crack structure of intact rock are systematically investigated by using advanced video microscope, electronic microscope and graphic analysis technology. The fractal effects of the discontinuous structure on the macro-mechanical behavior are discussed. Damage evolution in rocks is described by means of statistical mathematics. Based on the fractal distribution of cracks and on the theory of the weakest link, a general statistical formula of rock strength under a complex stress state has been developed, of which the influence of orientation distribution of cracks and irregularity of crack growth on rock strength has been taken into account. The new expression for rock strength reflects the collective effects of the scale of crack distribution, crack orientation distribution and the irregularity of crack surfaces on rock strength. It relates the macro-strength of rocks to its intrinsic structural properties. It is shown that the Weibull strength formula is a special case of the statistical strength expression when the orientational distribution of cracks is neglected. (C) 2000 Elsevier Science Ltd. All rights reserved.