Self-similarity in rock cracking and related complex critical exponents

The purpose of this paper is to further confirm some interpretations we made previously from materials or rock structure in term of the requirement of the introduction of complex critical exponents, where catastrophic brittle fracture is considered as a kind of second-order phase transition by analogy with percolation phenomenon. We propose here, using acoustic emission measurement data, a more complete experimental validation to support our previous conjecture that, “the higher the grain size and power supply, the longer range the interaction, and therefore the higher the imaginary part of complex critical exponents,” [Moura, A., Lei, X.L, Nishizawa, O., 2005. Prediction scheme for the catastrophic failure of highly loaded brittle materials or rocks. J. Mech. Phys. Solids 53(11), 2435–2455].