Criterion for fracture transition to critical stage

We have developed an analysis of data obtained in laboratory investigations of deformation of rocks by acoustic emission and X-ray microtomography. We found that defect accumulation occurs in fundamentally differing manners during loadin'g. At first, defects are generated randomly and have a specific size determined by a typical structural element of a material (e.g., a grain in granite). Then the defects with sizes not dictated by the material structure are generated. The interaction between these defects gives rise to critical defects that are capable of self-development. In all probability, a sample breakdown results from the evolution of the ensemble of critical defects. We found that the fracture stages can be distinguished by the type of energy distribution function of the acoustic emission signals. At the first stage, the distribution is approximated by an exponential function, whereas the second stage is characterized by a power-law function that points to a self-organized criticality state. This approach allows an early prediction (at early stages of deformation) of the spatial region in which a fault can be formed.