Progressive failure characteristics of different rock types through fractal analysis

The deformation and failure processes of rocks under stress are primarily induced by microcracking. Detecting this micro-interaction phenomenon before the ultimate failure has paramount importance for predicting the post-failure rock damage characteristics. In this study, we aim to quantify the evolution of microcracking through fractal analyses of scanning electron microscope (SEM) images, captured from three different rock types subjected to uniaxial loading at various stress levels. In terms of uniaxial compressive (UCS) and tensile strength (UTS) values, the rocks range from the strongest to the weakest as being diabase, ignimbrite, and marble, respectively.  All rock samples are uniaxially loaded up to critical stress thresholds as crack initiation (σ_ci), crack damage (σ_cd), and peak stress (σ_p) levels, considering their pre-defined characteristic stress-strain curves. Using the box-counting technique, the fractal dimension values (D_B) of cracking intensity, induced by loading are determined for all these three stages. Here, it should be noted that higher fractal dimensions represent more intense microcracking according to the fractal theory. The results show that the D_B values are increasing with the increasing amount of microcracks and the greatest D_B values are calculated for Diabase due to its highest strength ratio (UCS/UTS). Although the marble has the weakest strength values, it presents a higher D_B value than that of ignimbrite (D_Bmarble = 1.215 and D_Bignimbrite = 1.133) once the σ_cd stress threshold is reached. Furthermore, the D_Bmarble value is also greater than the D_Bignimbrite value for the σ_p stress level. It is because marble has a higher UCS/UTS ratio than the ratio of ignimbrite. Our results highlight the important role of rock texture on brittleness which exerts a primary control on fractal dimensions (D_B). A decrease in volumetric rigidity is more dramatic in marble than in ignimbrite with incremental loading. The insights provide a better understanding of the microcracking process that leads to macro-scale deformations in rock engineering.