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Abstract The onset of brittle failure in rocks includes dilatancy and strain localization. To better understand this nucleation process, we analyze the evolution of the local three‐dimensional strain tensor using X‐ray tomograms acquired during triaxial compression experiments on granite and sandstone. The onset of the localization of the compaction, dilation, and shear strain occurs when ∼65% of the rock volume experiences dilation. Tracking the locations of the high strains throughout loading suggests that the deformation that occurs early in loading influences the location of the system‐sized fracture network that produces macroscopic failure. This influence is larger in the sandstone experiments than the granite experiments, likely due to the microstructure of the sandstone. These results have important implications for detecting precursors to catastrophic failure.

Unraveling the details of fracture propagation leading to catastrophic rock failure is critical for understanding the precursors to earthquakes. Here we present numerical simulations of fracture growth using a work optimization criterion. These simulations apply work optimization to fracture propagation by finding the propagation orientation that minimizes the external work at each increment of fracture growth, repeating this process for each growing fracture tip in the model. We simulate published uniaxial compression experiments performed on a cylinder of marble with pre-cut fractures of varied lengths, orientations, and positions. This suite of experiments provides an ideal benchmark for the numerical simulations because of the relatively simple boundary conditions and the range of pre-cut fracture geometries that focus deformation. We compare the results of homogeneous, isotropic model material to results that incorporate hundreds of small randomly oriented and distributed microcracks representing internal weaknesses, such as grain boundaries. From these numerical models, we find that slip on and propagation of microcracks governs the non-linear stress-strain response observed before failure under axial compression. We use a suite of Monte Carlo realizations incorporating different initial seeding of microcracks to explore the range of fracture propagation paths that might result from inherent variation between rock samples. We find that while models that include microcracks begin to propagate fractures at smaller cumulative axial strains than an equivalent homogeneous isotropic model, ultimately, models including heterogeneity require more energy to reach failure than the homogeneous model. These results highlight the critical role of heterogeneity, such as microcracks, within the processes leading up to failure.

We quantify the spatial distribution of fracture networks throughout six in situ X-ray tomography triaxial compression experiments on crystalline rocks at confining stresses of 5–35 MPa in order to quantify how fracture development controls the final macroscopic failure of the rock, a process analogous to those that control geohazards such as earthquakes and landslides. Tracking the proportion of the cumulative volume of fractures with volumes >90th percentile to the total fracture volume, ∑v90/vtot indicates that the fracture networks tend to increase in localization toward these largest fractures for up to 80% of the applied differential stress. The evolution of this metric also matches the evolution of the Gini coefficient, which measures the deviation of a population from uniformity. These results are consistent with observations of localizing low magnitude seismicity before large earthquakes in southern California. In both this analysis and the present work, phases of delocalization interrupt the general increase in localization preceding catastrophic failure, indicating that delocalization does not necessarily indicate a reduction of seismic hazard. However, the proportion of the maximum fracture volume to the total fracture volume does not increase monotonically. Experiments with higher confining stress tend to experience greater localization. To further quantify localization, we compare the geometry of the largest fractures, with volumes >90th percentile, to the best fit plane through these fractures immediately preceding failure. The r2 scores and the mean distance of the fractures to the plane indicate greater localization in monzonite than in granite. The smaller mean mineral diameter and lower confining stress in the granite experiments may contribute to this result. Tracking these various metrics of localization reveals a close association between macroscopic yielding and the acceleration of fracture network localization. Near yielding, ∑v90/vtot and the Gini coefficient increase while the mean distance to the final failure plane decreases. Macroscopic yielding thus occurs when the rate of fracture network localization increases.