Application of Percolation Theory to Rock Damage and Fracture

Rock is a kind of complex and high-disordered geological material, its damage and fracture process usually shows obvious criticality. In this paper, percolation theory is applied to analyze and describe this critical property. First, we discuss the critical fracture probability of rock through percolation and renormalization analysis, and present the equivalence between fracture probability and damage variable. Based on scaling law and the relationship between critical exponents, a critical fractal dimension is obtained. Furthermore, according to the analysis of relationship between damage and fractal dimension, we suggest a damage-fractal formula, ω=ω0+ (D-D0)/Dc. This formula can not only be used to describe the damage evolution through the variation of fractal dimension, but also to define initial damage in rock. Finally, the theoretical conclusions are validated by a series of model experiments, and the experimental results agree with that of theoretical.