The spatial organization of deformation may provide key information about the timing of catastrophic failure in the brittle regime. In an ideal homogenous system, deformation may continually localize toward macroscopic failure, and so increasing localization unambiguously signals approaching failure. However, recent analyses demonstrate that deformation, including low magnitude seismicity, and fractures and strain in triaxial compression experiments, experience temporary phases of delocalization superposed on an overall trend of localization toward large failure events. To constrain the conditions that promote delocalization, we perform a series of X-ray tomography experiments at varying confining stresses (5-20 MPa) and fluid pressures (zero to 10 MPa) on Westerly granite cores with varying amounts of preexisting damage. We track the spatial distribution of the strain events with the highest magnitudes of the population within a given time step. The results show that larger confining stress promotes more dilation, and promotes greater localization of the high strain events approaching macroscopic failure. In contrast, greater amounts of preexisting damage promote delocalization. Importantly, the dilative strain experiences more systematic localization than the shear strain, and so may provide more reliable information about the timing of catastrophic failure than the shear strain.

Faults in carbonate rocks show both seismic and aseismic deformation processes, leading to a wide range of slip velocities. We deformed two centimeter-scale cores of Carrara marble at 25°C, under in-situ conditions of stress of 2-3 km depth, and imaged the nucleation and growth of creeping faults using dynamic synchrotron X-ray microtomography with micrometer spatial resolution. The first sample was under a constant confinement of 30 MPa and no pore fluid. The second sample was under a confinement in the range 35-23 MPa, with 10 MPa pore fluid pressure. We increased the axial stress by steps until creep deformation occurred and imaged deformation in 4D during creep. The samples deformed with a steady-state strain rate when the differential stress was constant, a process called creep. However, for both samples, we also observed transient events that include the acceleration of creep, i.e., creep bursts, phenomena similar to slow slip events that occur in continental active faults. During these transient creep events, strain rates increase and correlate in time with strain localization and the development of system-spanning fault networks. In both samples, the acceleration of opening and shearing of microfractures accommodated creep bursts. Using high-resolution time-lapse X-ray micro-tomography imaging, and digital image correlation, during triaxial deformation allowed quantifying creep in laboratory faults at sub-grain spatial resolution, and demonstrates that transient creep events (creep bursts) correlate with the nucleation and growth of faults.

Approximating the three-dimensional structure of a fault network at depth in the subsurface is key for robust estimates of fluid flow. However, only observations of two-dimensional outcrops are often available. To shed light on the relationship between two- and three-dimensional measurements of fracture networks, we examine data from a unique set of eleven X-ray synchrotron triaxial compression experiments that reveal the evolving three-dimensional fracture network throughout loading. Using machine learning, we derive relationships between the two- and three-dimensional measurements of three properties that control fluid flow: the porosity, and volume and tortuosity of the largest fracture at a particular differential stress step. The models predict the porosity and volume of the largest fracture with R2 scores of >0.99, but predict the tortuosity with maximum R2 scores of 0.68. To test the assumption that different rock types may require different equations between the two- and three-dimensional properties, we develop models for both individual rock types (granite, monzonite, marble, sandstone) and all of the experiments. Models developed using all of the experiments perform better than models developed for individual rock types, suggesting fundamental similarities between fracture networks in rocks often analyzed separately. Models developed with several parallel two-dimensional observations perform similarly to models developed with several perpendicular two-dimensional observations. When the models are developed with statistics of the two-dimensional observations, the models primarily depend on the mean and median when they predict the porosity, and minimum when they predict the volume and tortuosity.

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 >90th 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 >90th percentile immediately preceding failure, and calculate the distance between these fractures and the plane, and the r2 score of the fractures and the plane throughout each experiment. The r2 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.

Two key parameters control the localization of deformation and seismicity along and surrounding crustal faults: the strength and roughness of the preexisting fault surface. Using three-dimensional discrete element method simulations, we investigate how the anisotropy and amplitude of roughness control the mechanical behavior of healed faults within granite blocks during quasi-static triaxial compression. The results show that the localization of fracture development into a damage zone surrounding the initially weak fault zone coincides with the macroscopic failure of the rock. Rougher faults produce more gouge than smoother faults, providing an explanation for the weak influence of roughness on compressive strength. The particles within smoother fault zones slip with higher maximum fault-parallel velocities than rougher faults during the quasi-static loading, likely because the asperities do not impede slip as effectively in the smoother fault zone. The maximum fault-parallel velocity occurs after the peak stress, and falls to a steady state value by the end of the simulation, highlighting the non-constant evolution of slip despite the constant axial strain rate loading conditions. Smoother faults develop stronger correlations between the fault topography and fault slip magnitudes, likely because smoother faults experience higher velocities than rougher faults. Thus, fault surface asperities control slip by acting as speed bumps that hinder fault-plane parallel slip and promote fault-plane normal opening. These numerical models provide insights into the evolution of damage localization, fault roughness, gouge production, asperity abrasion, fault slip and stress concentrations along initially healed faults of varying roughness.