Linear fractal evolution characteristics of rock crack distributions during loading process

Abstract

To investigate the fractal characteristics of rock crack distributions during the loading process, discrete element method was used to make rock samples with joints and record the crack propagation. The Box-counting method was used to quantitatively analyze the fractal dimension of the crack distribution at each moment, and the relationship between the crack fractal dimension and strain ratio was established based on fractal theory. The results indicated that the relationship between the fractal dimension of the crack distribution and strain ratio showed a strong linear characteristic. By transforming this linear relationship into a linear function, the slope of the function was found to be linked to the failure patterns of the sample, and a refinement coefficient (damage-fracture reduction factor) was identified from the slope as an effective basis for determining the degree of sample damage and fracture. The damage-fracture reduction factor can be categorized: 0.25–0.5 (spilt and fracture), 0.5–0.9 (synergy between fracture and damage), 0.9–1 (microcrack asymptotic damage). Owing to the linear fractal characteristics, an expression for the damage variables influenced by failure patterns can be established from the geometric aspect. In addition, the linear fractal characteristics of the cracks were verified in other acoustic emission and crack extension experiments.