Fracture network localization preceding catastrophic failure

We quantify the evolving spatial distribution of fracture networks
throughout six in situ X-ray tomography triaxial compression experiments
on monzonite and granite at confining stresses of 5-35 MPa. We first
assess whether one dominant fracture continually grows at the expense of
others by tracking the proportion of the maximum fracture volume to the
total fracture volume. This metric does not increase monotonically. We
next examine if the set of the largest fractures continually dominates
deformation by tracking the proportion of the cumulative volume of
fractures with volumes >90^{th} percentile
to the total fracture volume. This metric indicates that the fracture
networks tend to increase in localization toward the largest set of
fractures for up to 80% of the experimental time (differential stress),
consistent with observations from southern California of localizing and
delocalizing seismicity. Experiments with higher confining stress tend
to have greater localization. To further assess the fracture networks
localization, we compare the geometry of the set of the largest
fractures to a plane. We find the best fit plane through the fractures
with volumes >90^{th} percentile immediately
preceding failure, and calculate the distance between these fractures
and the plane, and the r^{2} score of the fractures and
the plane throughout each experiment. The r^{2} scores
and the distance indicate greater localization in the monzonite
experiments than in the granite experiments. The smaller mean grain size
of the minerals in the granite may produce more sites of fracture
nucleation and termination, leading to more delocalized fracture
networks that deviate further from a plane. The higher applied confining
stress in the monzonite experiments (25-35 MPa) relative to the granite
experiments (5-10 MPa) may also contribute to the more localized
fracture networks in the monzonite experiments. The evolution of the
clustering the fractures toward the plane and the Gini coefficient,
which measures the deviation of a population from uniformity, closely
match each other. Tracking these metrics of localization also reveals
that macroscopic yielding appears to occur when the rate of fracture
network localization increases.