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 (σci), crack damage (σcd), and peak stress (σp) levels, considering their pre-defined
characteristic stress-strain curves. Using the box-counting technique, the fractal dimension values
(DB) 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 DB values are increasing with the increasing
amount of microcracks and the greatest DB 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 DB value than that of ignimbrite (DBmarble = 1.215 and DBignimbrite = 1.133) once the σcd stress
threshold is reached. Furthermore, the DBmarble value is also greater than the DBignimbrite value for
the σp 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 (DB). 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.