The influence of spatial resolution and noise on fracture network properties calculated from X-ray microtomography data

Rock deformation experiments performed at X-ray synchrotrons provide unique insights into the nature of fracture network development. However, these insights depend on the limitations of the X-ray tomography data. Here, we examine how spatial resolution and noise influence the calculated fracture network properties. To assess the influence of spatial resolution, we acquire two overlapping X-ray tomograms with spatial resolution that differ by an order of magnitude. To assess the influence of noise, we produce sets of synthetic tomograms with varying degrees of noise, including point-source noise and blurring noise. In the absence of noise, the differing spatial resolutions produce calculated porosities that differ by 0.05%, or 30% of the porosity measured in the high-resolution data. The fracture property that changes the most in the datasets of varying resolution is the fracture surface area, rather than the volume, length, or aperture. The two types of noise influence the porosity and fracture characteristics in opposite ways. In the synthetic tomograms in which higher values indicate fractures, added point noise increases the porosity while blurring noise decreases the porosity. In volumes with a mapping of gray values in which fractures have lower values, this trend would be reversed. This study is the first to quantify differences in fracture network properties extracted from X-ray tomograms due to spatial resolution and noise

Linking macroscopic failure with micromechanical processes in layered rocks: How layer orientation and roughness control macroscopic behavior

To constrain the impact of preexisting mechanical weaknesses on strain localization culminating in macroscopic shear failure, we simulate triaxial compression of layered sedimentary rock using three-dimensional discrete element method simulations. We develop a novel particle packing technique that builds layered rocks with preexisting weaknesses of varying orientations, roughness, and surface area available for slip. We quantify how the geomechanical behavior, characterized by internal friction coefficient, μ0, and failure strength, σF, vary as a function of layer orientation, θ, interface roughness, and total interface area. Failure of the simulated sedimentary rocks mirrors key observations from laboratory experiments on layered sedimentary rock, including minima σF and μ0 for layers oriented at 30° with respect to the maximum compressive stress, σ1, and maxima σF and μ0 for layers oriented near 0° and 90° to σ1. The largest changes in σF (66%) and μ0 (20%) occur in models with the smoothest interfaces and largest interface area. Within the parameter space tested, layer orientation exerts the most significant impact on σF and μ0. These simulations allow directly linking micromechanical processes observed within the models to macroscopic failure behavior. The spatial distributions of nucleating microfractures, and the rate and degree of strain localization onto preexisting weaknesses, rather than the host rock, are systematically linked to the distribution of failure strengths. Preexisting weakness orientation more strongly controls the degree and rate of strain localization than the imposed confining stress within the explored parameter space. Using the upper and lower limits of μ0 and σF obtained from the models, estimates of the Coulomb shear stress required for failure of intact rock within the upper seismogenic zone (7 km) indicates that a rotation of 30° of σ1 relative to the weakness orientation may reduce the shear stress required for failure by up to 100 MPa

Competition between slow slip and damage on and off faults revealed in 4D synchrotron imaging experiments

In the continental crust, faults may accommodate deformation through aseismic creep, slow slip events, or seismic slips that produce dynamic damage, or a combination of these endmembers. A variety of parameters controls the occurrence of these mechanical behaviors. In a series of laboratory experiments, we image centimeter-scale faults during sliding under in situ conditions. We perform four experiments of slip on centimeter-scale crystalline rock samples prepared with a saw-cut interface at 45° from the direction to the maximum compressive stress and at stress conditions of 2–3 km depth. We image fault slip and off-fault fracture development using 4D synchrotron X-ray microtomography. Three faults have an initial rough interface, and deformation occurs with increasing differential stress by a combination of slow slip events and off-fault damage, until catastrophic failure and the formation of new faults. Conversely, the pre-cut fault with a smooth initial surface deforms mainly by slow slip, develops numerous striations along its slip plane, and no microfractures are detected in the wall rock. Our experiments reproduce aseismic and seismic faulting behavior, and demonstrate that the roughness of the fault plane is one of the parameters that control the transition between these two behaviors. A fault with a rougher interface may tend to develop more off-fault damage and seismic behavior. For the rough fault experiments, the secondary faulting occurs along a network of faults oriented at high angles from the pre-existing saw-cut plane, a behavior similar to several earthquake sequences that occurred along orthogonal faults

Fracture Network Localization Preceding Catastrophic Failure in Triaxial Compression Experiments on Rocks

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

The mixology of precursory strain partitioning approaching brittle failure in rocks

SUMMARY We examine the strain accumulation and localization process throughout 12 triaxial compression experiments on six rock types deformed in an X-ray transparent apparatus. In each experiment, we acquire 50–100 tomograms of rock samples at differential stress steps during loading, revealing the evolving 3-D distribution of X-ray absorption contrasts, indicative of density. Using digital volume correlation (DVC) of pairs of tomograms, we build time-series of 3-D incremental strain tensor fields as the rocks are deformed towards failure. The Pearson correlation coefficients between components of the local incremental strain tensor at each stress step indicate that the correlation strength between pairs of local strain components, including dilation, contraction and shear strain, are moderate-strong in 11 of 12 experiments. In addition, changes in the local strain components from one DVC calculation to the next show differences in the correlations between pairs of strain components. In particular, the correlation of the local changes in dilation and shear strain tends to be stronger than the correlation of changes in dilation-contraction and contraction-shear strain. In 11 of 12 experiments, the most volumetrically frequent mode of strain accommodation includes a synchronized increase in multiple strain components. Early in loading, under lower differential stress, the most frequent strain accumulation mode involves the paired increase in dilation and contraction at neighbouring locations. Under higher differential stress, the most frequent mode is the paired increase in dilation and shear strain. This mode is also the first or second most frequent throughout each complete experiment. Tracking the mean values of the strain components in the sample and the volume of rock that each component occupies reveals fundamental differences in the nature of strain accumulation and localization between the volumetric and shear strain modes. As the dilative strain increases in magnitude throughout loading, it tends to occupy larger volumes within the rock sample and thus delocalizes. In contrast, the increasing shear strain components (left- or right-lateral) do not necessarily occupy larger volumes and so involve localization. Consistent with these evolutions, the correlation length of the dilatational strains tends to increase by the largest amounts of the strain components from lower to higher differential stress. In contrast, the correlation length of the shear strains does not consistently increase or decrease with increasing differential stress

Volumetric and Shear Strain Localization in Mt. Etna Basalt

To examine the impact of preexisting weaknesses on fracture coalescence during volcanic edifice deformation, we triaxially compressed Mount Etna basalt while acquiring in situ dynamic X‐ray microtomograms and calculated the internal strain tensor fields using image correlation. Contraction localization preceded dilation and shear strain localization into the protofault zone. This onset of strain localization preceded macroscopic yielding and coincided with increases in the magnitude and volume of rock experiencing dilation, and spatial clustering of the strain populations. The exploitation of weaknesses by propagating fractures enabled the dominant shear strain to switch senses as propagating fractures lengthened along 30–60° from σ1. Scanning electron microscopy images reveal pore‐emanated fractures, and fractures linking pores. These experiments provide evidence of internal contraction preceding dilation and shear, consistent with inferences from field and laboratory observations. The transition from contraction to dilation may provide a precursory signal of volcanic flank eruption

Creep Burst Coincident With Faulting in Marble Observed in 4-D Synchrotron X-Ray Imaging Triaxial Compression Experiments

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 and imaged the nucleation and growth of faults using dynamic synchrotron X‐ray microtomography. The first sample experienced a constant confinement of 30 MPa and no pore fluid. The second sample experienced confinement in the range 35–23 MPa and water as a pore fluid at 10 MPa pore pressure. We increased the axial stress by steps until creep deformation occurred and imaged deformation in 4‐D. The samples deformed with a quasi‐constant or increasing 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, that is, 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 slow development of system‐spanning fault networks. In both samples, the acceleration of opening and shearing of microfractures accommodated creep bursts. High‐resolution time‐lapse X‐ray microtomography imaging and digital image correlation during triaxial deformation quantify creep in laboratory faults at subgrain spatial resolution. This work demonstrates that transient creep events, that is, creep bursts or slow slip events, correlate with the nucleation and slow growth of faults and not only with slip on preexisting faults

The evolving energy budget of experimental faults within continental crust: Insights from in situ dynamic X-ray microtomography

We investigate the evolving distribution of strain produced by a sliding fault within intact crystalline rock, and the energetics of deformation that occur both on- and off-fault. We slid precut faults of differing roughness oriented at 45° to while acquiring in situ X-ray microtomograms. Digital volume correlation of tomograms provide estimates of the 3D displacement and strain fields. This characterization of the strain tensor field reveal that the differing fault roughness produced distinct slip behavior, degree of strain localization and accumulation, and energy budget partitioning. The rougher fault slipped more episodically, hosted a wider and more asymmetric damage zone, and accommodated less normal and shear strain. This fault consumed more energy in off-fault deformation (Wint) per volume and more energy in frictional slip (Wfric) as portions of the total energy input to the system (Wext) than the smoother fault. In both experiments, Wfric consumed the largest portion of the energy budget (50–100%), while Wint consumed smaller percentages (5–20%). Tracking the temporal variability of energy partitioning revealed how evolving fault architecture determined the energetic dominance of particular deformational processes, and so highlighted the importance of tracking energy partitioning through time

Predicting the proximity to macroscopic failure using local strain populations from dynamic in situ X-ray tomography triaxial compression experiments on rocks

Predicting the proximity of large-scale dynamic failure is a critical concern in the engineering and geophysical sciences. Here we use evolving contractive, dilatational, and shear strain deformation preceding failure in dynamic X-ray tomography experiments to examine which strain components best predict the proximity to failure. We develop machine learning models to predict the proximity to failure using time series of three-dimensional local incremental strain tensor fields acquired in rock deformation experiments under stress conditions of the upper crust. Three-dimensional scans acquired in situ throughout triaxial compression experiments provide a distribution of density contrasts from which we estimate the three-dimensional incremental strain that accumulates between each scan acquisition. Training machine learning models on multiple experiments of six rock types provides suites of feature importance that indicate the predictive power of each feature. Comparing the average importance of groups of features that include information about each strain component quantifies the ability of the contractive, dilatational and shear strain to predict the proximity of macroscopic failure. A total of 24 models of four machine learning algorithms with six rock types indicate that 1) the dilatational strain provides the best predictive power of the strain components, and 2) the intermediate values (25th-75th percentile) of the strain population provide the best predictive power of the statistics of the strain populations. In addition, the success of the predictions of models trained on one rock type and tested on other rock types quantifies the similarities and differences of the precursory strain accumulation process in the six rock types. These similarities suggest the potential existence of a unified theory of brittle rock deformation for a range of rock types

Isolating the factors that govern fracture development in rocks throughout dynamic in situ X-ray tomography experiments

Centuries of work have highlighted the importance of several characteristics on fracture propagation. However, the relative importance of each characteristic on the likelihood of propagation remains elusive. We rank this importance by performing dynamic X‐ray microtomography experiments that provide unique access to characteristics of evolving fracture networks as rocks are triaxially compressed toward failure. We employed a machine learning technique based on logistic regression analysis to predict whether or not a fracture grows from 14 fracture geometry and network characteristics identified throughout four experiments on crystalline rocks in which thousands of fractures propagated. The characteristics that best predict fracture growth are the length, thickness, volume, and orientation of fractures with respect to the external stress field and the distance to the closest neighboring fracture. Growing fractures tend to be more clustered, shorter, thinner, volumetrically smaller, and dipping closer to 30–60° from the maximum compression direction than closing fractures