A MODEL FOR CRACK CONNECTIVITY IN ROCKS, A DISCUSSION

We reanalyzed a model introduced by T. R. Madden for the evaluation of the state of connectivity among the microcrack population existing in side crystalline rocks. The model assumes that cracks are distributed randomly in a cubic lattice with a basic occupation probability, p. De pending on the value of p, the state of connectivity can give rise to macroscopic paths, which allow electrical conduction of the sample, or to extended crack surfaces, which would be responsible for rock failu re. nle position of the phase boundaries, that is, the threshold value s of p for the onset of conductivity or macroscopic fracture, are esti mated by a real-space renormalization-group (RG) technique. By identif ying all the relevant configurations of the lattice model, we have bee n able to provide explicit analytic formulae for the critical lines. T he criterion used by Madden to ''accept'' the existence of microscopic linear connectivity is modified and the new consequences discussed. m e analyze the limitations of simple versions of the RG technique, in p articular when concerned with anisotropic spatial distributions of cra cks. Finally, we emphasize the interest of acquiring experimental data , especially to test the position of the conduction thresholds.