Characteristics of fractal and percolation of rocks subjected to uniaxial compression during their failure process

The formation process of the cracks in the rocks,including the initiation,propagation and coalescence of the micro-cracks,was of statistical fractal features.It was considered that the failure of the elements would cause acoustic emission and micro-cracks which led to gradual damage of the rocks.The fractal model and percolation model were established by statistically analyzing the spatial distribution of the failure elements and AE event locations.The evolution of fractal dimensions and percolation were obtained by simulating the failure process of the heterogeneous rock samples with a numerical code RFPA3D.The fractal and percolation features of the micro-fractures were obviously influenced by heterogeneities.During the complete loading process,the fractal dimension decreased with the increase of the heterogeneity and the uniaxial compressive strength of the rock samples.There was an increase tendency of the number of failure clusters and fractal dimensions at the first loading stage.When the peak value of the loading was reached,the fractal dimensions increased to a certain value and the number of the failure clusters abruptly decreased due to the combination of the small failure clusters into large clusters.It was shown that the fractal and percolation features were formed due to the self-familiarity of the rock materials at different scale levels.