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The progressive localization of deformation has long been recognized as a fundamental phenomenon of the macroscopic failure of rocks. Our recent analyses using X-ray tomography during triaxial compression indicate that fractures and higher magnitudes of shear and dilative strain spatially localize as rocks are driven closer to macroscopic failure. Similarly, geophysical observations of low magnitude seismicity in southern and Baja California show that deformation localizes toward the future rupture plane of M>7 earthquakes. These sets of observations indicate that deformation can increase in localization toward failure, and that deformation can temporarily decrease in localization (delocalize) during this overall increase. These observations indicate that the spatial organization of deformation may be used to recognize the acceleration of the precursory phase leading to large earthquakes and the macroscopic, system-scale failure of heterogeneous materials. However, such efforts will require identifying the conditions that promote phases of delocalization, and how these perturbations in the overall trend of increasing localization influence the timing of macroscopic failure. In this presentation, I will describe these analyses, and new work that aims to identify which characteristics of the fracture networks determine the localization at a particular level of stress, and the change in localization from one stress step to the next in triaxial compression experiments at the confining stress conditions of the upper crust.

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.

Determining how fracture network development leads to macroscopic failure in heterogeneous materials may help estimate the timing of failure in rocks in the upper crust as well as in engineered structures. The proportion of extensile and shear deformation produced by fracture development indicates the appropriate failure criteria to apply, and thus is a key constraint in such an effort. Here, we measure the volume proportion of extensile and shear fractures using the orientation of the fractures that develop in triaxial compression experiments in which fractures are identified using dynamic in situ synchrotron X-ray imaging. The fracture orientations transition from shear to extensile approaching macroscopic, system-size failure. Numerical models suggest that this transition occurs because the fracture networks evolve in order to optimize the total mechanical efficiency of the system. Our results provide a physical interpretation of the empirical internal friction coefficient in rocks.

The geometric properties of fractures influence whether they propagate, arrest, or coalesce with other fractures. Thus, quantifying the relationship between fracture network characteristics may help predict fracture network development, and perhaps precursors to catastrophic failure. To constrain the relationship and predictability of fracture characteristics, we deform eight one centimeter tall rock cores under triaxial compression while acquiring in situ X-ray tomograms. The tomograms reveal precise measurements of the fracture network characteristics above the spatial resolution of 6.5 µm. We develop machine learning models to predict the value of each characteristic using the other characteristics, and excluding the macroscopic stress or strain imposed on the rock. The models predict fracture development more accurately in the experiments performed on granite and monzonite, than the experiments on marble. Fracture network development may be more predictable in these igneous rocks because their microstructure is more mechanically homogeneous than the marble, producing more systematic fracture development that is not strongly impeded by grain contacts and cleavage planes. The varying performance of the models suggest that fracture volume, length, and aperture are the most predictable of the characteristics, while fracture orientation is the least predictable. Orientation does not correlate with length, as suggested by the idea that the orientation evolves with increasing differential stress and thus fracture length. This difference between the observed and expected relationship between orientation and length highlights the influence of mechanical heterogeneities and local stress perturbations on fracture growth as fractures propagate, link, and coalesce.

The continuum of behavior that emerges during fracture network development in crystalline rock may be categorized into three end-member modes: fracture nucleation, isolated fracture propagation, and fracture coalescence. These different modes of fracture growth produce fracture networks with distinctive geometric attributes, such as clustering and connectivity, that exert important controls on permeability and the extent of fluid–rock interactions. To track how these modes of fracture development vary in dominance throughout loading toward failure and thus how the geometric attributes of fracture networks may vary under these conditions, we perform in situ X-ray tomography triaxial compression experiments on low-porosity crystalline rock (monzonite) under upper-crustal stress conditions. To examine the influence of pore fluid on the varying dominance of the three modes of growth, we perform two experiments under nominally dry conditions and one under water-saturated conditions with 5 MPa of pore fluid pressure. We impose a confining pressure of 20–35 MPa and then increase the differential stress in steps until the rock fails macroscopically. After each stress step of 1–5 MPa we acquire a three-dimensional (3D) X-ray adsorption coefficient field from which we extract the 3D fracture network. We develop a novel method of tracking individual fractures between subsequent tomographic scans that identifies whether fractures grow from the coalescence and linkage of several fractures or from the propagation of a single fracture. Throughout loading in all of the experiments, the volume of preexisting fractures is larger than that of nucleating fractures, indicating that the growth of preexisting fractures dominates the nucleation of new fractures. Throughout loading until close to macroscopic failure in all of the experiments, the volume of coalescing fractures is smaller than the volume of propagating fractures, indicating that fracture propagation dominates coalescence. Immediately preceding failure, however, the volume of coalescing fractures is at least double the volume of propagating fractures in the experiments performed at nominally dry conditions. In the water-saturated sample, in contrast, although the volume of coalescing fractures increases during the stage preceding failure, the volume of propagating fractures remains dominant. The influence of stress corrosion cracking associated with hydration reactions at fracture tips and/or dilatant hardening may explain the observed difference in fracture development under dry and water-saturated conditions.

SUMMARY Two key parameters control the localization of deformation and seismicity along and surrounding crustal faults: the strength and roughness of the pre-existing fault surface. Using 3-D discrete element method simulations, we investigate how the anisotropy and amplitude of roughness control the mechanical behaviour of healed faults within granite blocks during quasi-static triaxial compression. We focus on models in which the uniaxial compressive strength of the healed faults is about 25 per cent of that strength of the surrounding host rock. These models provide insights into the evolution of fracture network localization, fault roughness, gouge production, fault slip and stress concentrations along initially healed faults of varying roughness. In contrast to expectations, the uniaxial compressive strengths of models that host faults with root-mean-squared roughness amplitudes of 0.2–1.4 mm do not vary more than the change produced by variations in particle packing. To assess if this lack of influence arises from the evolving roughness of the faults, we track the roughness amplitudes parallel and perpendicular to the downdip direction throughout fault failure and slip. The de facto roughness does not provide an explanation for the lack of influence of roughness on compressive strength because the roughness of the faults does not evolve to similar values with slip. Rather, smoother faults remain smoother than rougher faults throughout the simulation. However, the rougher faults produce larger volumes of gouge than the smoother faults. The gouge lubricates the fault and thereby reduces the influence of roughness on compressive strength. These observations suggest that fault topography and the asperities that build this topography do not exert a significant impact on deformation. To quantify the influence of asperities on slip, we calculate correlation coefficients between the fault surface topography and components of the slip vectors. The observed negative correlation coefficients between the fault topography and fault-plane parallel slip quantify the degree to which asperities slow slip in the downdip direction. The observed positive correlation coefficients between the topography and fault-plane perpendicular movement quantify the degree to which asperities promote opening. Thus, this analysis shows how asperities control slip by acting as speed bumps that hinder fault-plane parallel slip and promote fault-plane normal opening as the healed faults slide. The asperities do not significantly control fault movement during the unlocking and failure of the healed faults, but only following the peak axial stress as the faults slide and damage zones develop. These models thus provide unparalleled access to the dynamics of reactivated healed faults.

SUMMARYWe 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.

Understanding the mechanisms of strain localization leading to brittle failure in reservoir rocks can shed light on geomechanical processes such as porosity and permeability evolution during rock deformation, induced seismicity, fracturing, and subsidence in geological reservoirs. We perform triaxial compression tests on three types of porous reservoir rocks to reveal the local deformation mechanisms that control system-size failure. We deformed cylindrical samples of Adamswiller sandstone (23% porosity), Bentheim sandstone (23% porosity), and Anstrude limestone (20% porosity), using an X-ray transparent triaxial deformation apparatus. This apparatus enables the acquisition of three-dimensional synchrotron X-ray images, under in situ stress conditions. Analysis of the tomograms provide 3D distributions of the microfractures and dilatant pores from which we calculated the evolving macroporosity. Digital volume correlation analysis reveals the dominant strain localization mechanisms by providing the incremental strain components of pairs of tomograms. In the three rock types, damage localized as a single shear band or by the formation of conjugate bands at failure. The porosity evolution closely matches the evolution of the incremental strain components of dilation, contraction, and shear. With increasing confinement, the dominant strain in the sandstones shifts from dilative strain (Bentheim sandstone) to contractive strain (Adamswiller sandstone). Our study also links the formation of compactive shear bands with porosity variations in Anstrude limestone, which is characterized by a complex pore geometry. Scanning electron microscopy images indicate that the microscale mechanisms guiding strain localization are pore collapse and grain crushing in sandstones, and pore collapse, pore-emanated fractures and cataclasis in limestones. Our dynamic X-ray microtomography data brings unique insights on the correlation between the evolutions of rock microstructure, porosity evolution, and macroscopic strain during the approach to brittle failure in reservoir rocks.

Examining the deformation of rocks during triaxial compression may provide insights into the precursory phase that leads to large earthquakes by revealing the components of the deformation field that evolve with predictable, systematic behavior preceding catastrophic failure. Here, we build three-dimensional discrete element method simulations of the triaxial compression of rock cores that include a variety of fault geometries in order to identify the components of the deformation field, including the velocity and strain components, that enable machine learning models to predict the timing of macroscopic failure. The results suggest that the velocity field provides more valuable information about the timing of macroscopic failure than the strain field, and in particular, the velocity component parallel to the maximum compression direction. The models also strongly depend on the second invariant of the strain deviator tensor, $${J}_{2}$$ J 2 , indicative of the shear strain. The importance of $${J}_{2}$$ J 2 on the model predictions increases with confining stress, consistent with laboratory observations that show a transition from tensile- to shear-dominated deformation with increasing confining stress. In contrast to expectations from previous machine learning analyses, none of the models strongly depend on components of the strain tensor indicative of dilation, such as the first invariant of the strain tensor. This difference may arise because the simulations host less dilative strain than the experimental rocks.

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 MP...

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.

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 σ 1 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.

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.

During fast and slow earthquakes deformation localizes along narrow and quasi-planar fault surfaces. However, processes controlling the localization process develop not only on the fault surface but also in the volume surrounding the fault zone. How these processes transition from a dispersed to more localized distribution of damage remains controversial. Moreover, to what degree the localization process controls the speed of coseismic slip is an open question. We perform a series of 4D X-ray microtomography experiments on crystalline rocks (granite, marble), with and without a pre-existing slip surface, and image the development of damage while each sample is loaded until system-size brittle failure. We image and deform the samples under in situ stress conditions of a few kilometers depth using the Hades deformation apparatus installed on the tomography beamline ID19 at the European Radiation Synchrotron Facility. By imaging all the microfractures that develop in the samples, we characterize their individual geometry and the geometry of the entire microfracture network. The results show that, when a pre-existing slip surface exists in the sample, slow earthquakes can generate damage in the volume around the fault, leading to catastrophic faulting. When no pre-existing fault is present, microfractures accumulate and can lead to two end-member types of earthquakes. One type is a catastrophic failure of the sample that occurs when the microfractures link into a macroscopic fault, producing a fast earthquake. Alternatively, the microfractures can grow without significant fracture coalescence, leading to the slow development of a fault network with a transient increase of macroscopic deformation rate that resembles that of a slow earthquake. We conclude that damage coalescence influences the slow and fast behaviours of earthquake slip.

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.

International audience; Strain localisation structures, such as shear fractures and compaction bands, are of importance due to their influence on permeability and therefore outgassing, a factor thought to influence eruptive style. In this study, we aim to develop a better understanding of strain localisation in porous volcanic rocks using X-ray tomographic images of samples of porous andesite (porosity = 0.26) acquired before and after deformation in the brittle and ductile regimes. These 3D images have been first analysed to provide 3D images of the porosity structure within the undeformed andesite, which consists of a large, well-connected porosity backbone alongside many smaller pores that are either isolated or connected to the porosity backbone by thin microstructural elements (e.g., microcracks). Following deformation, porosity profiles of the samples show localised dilation (porosity increase) and compaction (porosity reduction) within the samples deformed in the brittle and ductile regimes, respectively. Digital volume correlation (DVC) of the images before and after triaxial deformation was used to quantify the tensor strain fields, and the incremental divergence (volumetric strain) and curl (used as an indicator of shear strain) of the displacement fields were calculated from the DVC. These fields show that strain localisation in the sample deformed in the brittle regime manifested as a ~ 1 mm-wide, dilatational shear fracture oriented at an angle of 40–45° to the maximum principal stress. Pre- and post-deformation permeability measurements show that permeability of the sample deformed in the brittle regime increased from 3.9 × 10−12 to 4.9 × 10−12 m2, which is presumed to be related to the shear fracture. For the sample deformed in the ductile regime, strain localised into ~1 mm-thick, undulating compaction bands orientated sub-perpendicular to the maximum principal stress with little evidence of shear. Taken together, our data suggest that these bands formed during large stress drops seen in the mechanical data, within high-porosity zones within the sample, and within the large, well-connected porosity backbone. Pre- and post-deformation permeability measurements indicate that inelastic compaction decreased the permeability of the sample by a factor of ~3. The data of this study assist in the understanding of strain localisation in porous volcanic rocks, its influence on permeability (and therefore volcanic outgassing), and highlight an important role for DVC in studying strain localisation in volcanic materials.

Different modes of fracture growth produce fracture networks with distinctive geometric attributes that exert important controls on the extent of fluid-rock interactions. We perform in situ X-ray tomography triaxial compression experiments on monzonite to investigate the influence of fracture nucleation, preexisting fracture propagation, and coalescence on fracture network development in crystalline rocks under crustal conditions. We impose a confining pressure of 20–35 MPa and then increase the differential stress in steps until the rock fails macroscopically. After each stress step we acquire a three-dimensional (3D) X-ray adsorption coefficient field from which we extract the 3D fracture network. To examine the influence of pore fluid on fracture network development, we perform two experiments under nominally-dry conditions and one under water-saturated conditions with 5 MPa pore fluid pressure. We develop a method of tracking individual fractures between subsequent tomographic scans that identifies whether fractures grow from the coalescence and linkage of several fractures or from the propagation of a single fracture. Throughout loading until shortly before failure in all of the experiments, the volume of coalescing fractures is smaller than the volume of propagating fractures, indicating that fracture propagation dominates coalescence. Immediately preceding failure, however, the volume of coalescing fractures is at least double the volume of propagating fractures in the experiments deformed at nominally dry conditions. In the water-saturated sample, although the volume of coalescing fractures increases during this stage, the volume of propagating fractures remains dominant. The influence of stress corrosion cracking associated with hydration reactions at fracture tips and/or dilatant hardening may explain the observed difference in fracture development under dry and water-saturated conditions. Our experimental data on fracture growth at different conditions provide new constraints in assessing fluid flow in subsurface fracture networks that are central to energy and environmental engineering practices.

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.

Predicting the onset of system-size failure in rocks represents a fundamental goal in assessing earthquake hazard. On the field, seismological, geodetic and other monitoring data may record precursors to earthquakes. In laboratory experiments, such precursors often rely on monitoring acoustic emissions and this technique has some limitations in terms of spatial resolution and the lack of detection of aseismic strain. To overcome these challenges, we have performed a series of forty rock deformation experiments where we imaged, using synchrotron X-ray microtomography, rock samples as they deformed until brittle failure, at in situ conditions of pressure, high spatial micrometer spatial resolution, and through time. On the one hand, direct processing of the X-ray tomograms allow visualizing how precursory microfractures nucleate, grow, and coalesce until failure. From these data, we propose to characterize brittle failure as a critical phase transition, with evidence of several power-laws that characterize fracture growth. On the other hand, digital volume correlation techniques quantify the evolution of the local strain field inside each sample. We analysed the statistical properties of these strain fields using several machine learning techniques to predict the main parameters that control fracture growth (length, volume, shape, distance to the nearest fracture), and the features of the strain field that best predict the distance to failure. Our rock deformation experimental results show that, under laboratory conditions, precursors to brittle deformation exist. These precursors show predictable evolution when approaching system-size brittle deformation and we demonstrate that specific components of the strain field characterize this evolution to failure.

A fundamental challenge in geophysics is predicting the timing of large earthquakes. A key step in addressing this problem is constraining the factors that indicate the timing of the next large rupture. To isolate the factors that help predict the proximity of the next earthquake, we develop machine learning models to predict the stress distance to macroscopic failure in triaxial compression X-ray tomography experiments on rocks at the stress conditions of the upper crust. In these experiments, we apply increasing axial stress in steps, and acquire a 3D X-ray tomogram at each stress step while the rock is under constant load, revealing the 3D density distribution. Segmenting the density fields provide the locations of rock (voxels dominated by solid), and pores and fractures (voxels dominated by air). We train the machine learning models using the geometry and clustering properties of the fracture networks identified in the tomography scans. We develop extreme gradient boosting (XGBoost) models to predict the stress distance to failure. In experiments on Carrara marble, monzonite, and granite, the models predict the stress distance to failure with r2 values > 0.7. We examine the feature importance to identify the factors that provide the best predictive power of the distance to failure. Measurements of the fracture network clustering and the shape anisotropy of fractures tend to have the highest importance of the features, providing greater predictive information than the fracture volume, fracture length, fracture aperture, and fracture orientation relative to the maximum compression direction.

Depleted oil reservoirs are considered a viable solution to the global challenge of CO2 storage. A key concern is whether the wells can be suitably sealed with cement to hinder the escape of CO2. Under reservoir conditions, CO2 is in its supercritical state, and the high pressures and temperatures involved make real-time microscopic observations of cement degradation experimentally challenging. Here, we present an in situ 3D dynamic X-ray micro computed tomography (μ-CT) study of well cement carbonation at realistic reservoir stress, pore-pressure, and temperature conditions. The high-resolution time-lapse 3D images allow monitoring the progress of reaction fronts in Portland cement, including density changes, sample deformation, and mineral precipitation and dissolution. By switching between flow and nonflow conditions of CO2-saturated water through cement, we were able to delineate regimes dominated by calcium carbonate precipitation and dissolution. For the first time, we demonstrate experimentally the impact of the flow history on CO2 leakage risk for cement plugging. In-situ μ-CT experiments combined with geochemical modeling provide unique insight into the interactions between CO2 and cement, potentially helping in assessing the risks of CO2 storage in geological reservoirs. This is an open access article published under a Creative Commons Attribution (CC-BY) License, which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.

Digital volume correlation analysis of time-resolved X-ray microtomography scans acquired during in situ triaxial compression of Green River shale cores provided time series of 3-D incremental strain fields that elucidated evolving deformation processes by quantifying microscopic strain localization. With these data, we investigated the impact of mechanical anisotropy on microscopic strain localization culminating in macroscopic shear failure. We conducted triaxial compression experiments with the maximum compressive stress, σ1, aligned perpendicular and parallel to lamination planes in order to investigate end-member stress states that arise within sedimentary basins. When the preexisting laminations were perpendicular to σ1, a lamination-parallel region with high axial compaction developed within the macroscopically linear deformation phase of the experiment and then thickened with increasing applied differential stress. Scanning electron microscopy images indicate that this axial compaction occurred within a lower density lamination and that more axial compaction occurred within the center of the core than near its sides. Boundary element method simulations suggest that this compacting volume promoted shear fracture development within the upper portion of the shale. When the laminations were parallel to σ1, lamination-parallel dilation bands formed, thickened, and intensified in dilation. Population densities of the distributions of incremental shear strain, radial dilation, and axial contraction calculated by digital volume correlation analysis enabled quantification of the evolving overall impact of, and interplay between, these various deformation modes. (Less)

The transition from stable to unstable fracture propagation occurs when fractures begin to interact and link. Thus, fracture network coalescence controls how rocks and engineered structures fail. To constrain the factors that influence localization in shear zones under brittle conditions, we build discrete element method models with a rough fault embedded in a shear zone. We add varying numbers of diffuse, randomly-placed weaknesses to examine the influence of diffuse damage on fracture network localization. The number of weaknesses controls the localization behavior of the fault network and the final fault geometry. We quantify localization using the Gini coefficient of the fracture volume, which measures the nonuniformity in a population. Each model generally increases in localization toward failure. However, models with more diffuse damage experience delocalization phases that are superimposed on the overall trend of increasing localization. The observed link between delocalization and host rock damage may help explain the varying localization of low magnitude seismicity in southern California. Models with more diffuse damage produce more complex fault geometries comprised of several parallel strands of wing cracks. The propagation of these wing cracks reduces the shear stress acting on the model boundaries, indicating that this fracture development increases the mechanical efficiency of the system.

Determining the difference in strength between a healed fault and surrounding rock that causes deformation to effectively ignore the fault is key for understanding earthquake mechanics. Here, we use three-dimensional discrete element method models to assess how varying degrees of fault healing influence the force and fracture network partitioning and architecture during triaxial compression. When the fault zone is 80% of the Uniaxial Compressive Strength (UCS) of the host rock, the system supports the same UCS as homogeneous models, and partitions deformation equally among the weaker fault and stronger host rock. The observed larger width of the damage zone surrounding less-optimally oriented faults supports the idea that the inherited geometric complexity of faults may be primarily responsible for the observed widening of the damage zone with displacement. Macroscopic failure in the models coincides in time with the highest rate of fracture development within the damage zone and host rock, rather than within the fault core. This result and the observed localization of fracture development toward the fault zone coincident with macroscopic failure suggest that efforts to recognize precursory signals before large earthquakes should monitor the geophysical changes in the volume of crust around the fault.

Recent geophysical imaging indicates that the Hayward Fault hard links to the Rodgers Creek Fault at 5m depth within the San Pablo Bay, CA, suggesting that earthquakes may be able to rupture continuously through the fault network. To investigate fault propagation, interaction, and linkage in segmented fault networks, including those within the San Pablo Bay, we simulate the development of two idealized, underlapping faults within an extensional step over at seismogenic depths using work optimization. We test the sensitivity of fault growth to strength anisotropy, material heterogeneities, and initial fault geometry. The optimal faults propagate toward each other until linking with the other fault at its tip and form a single hard-linked transverse fault. These faults propagate with relatively high propagation power or rate of efficiency gain. Less efficient faults form wider basins and develop with reduced propagation power. Models with initial fault geometries that more closely match the shallowly imaged Hayward and Rodgers Creek faults suggest that the faults link at seismogenic depths if a mapped segment of the Rodgers Creek that extends into the San Pablo Bay is currently inactive. Predictions of average slip rate, slip per earthquake, and earthquake magnitude from these models closely match paleoseismic estimates. The hard linkage of the Hayward and Rodgers Creek faults imaged in the near-surface, and predicted by these models, increases local seismic hazard by increasing the upper limit of throughgoing earthquakes to M 7.6.

We employ work optimization to predict the geometry of frontal thrusts at two stages of an evolving physical accretion experiment. Faults that produce the largest gains in efficiency, or change in external work per new fault area, ΔWext/ΔA, are considered most likely to develop. The predicted thrust geometry matches within 1 mm of the observed position and within a few degrees of the observed fault dip, for both the first forethrust and backthrust when the observed forethrust is active. The positions of the second backthrust and forethrust that produce >90% of the maximum ΔWext/ΔA also overlap the observed thrusts. The work optimal fault dips are within a few degrees of the faults dips that maximize the average Coulomb stress. Slip gradients along the detachment produce local elevated shear stresses and high strain energy density regions that promote thrust initiation near the detachment. The mechanical efficiency (Wext) of the system decreases at each of the two simulated stages of faulting and resembles the evolution of experimental force. The higher ΔWext/ΔA due to the development of the first pair relative to the second pair indicates that the development of new thrusts may lead to diminishing efficiency gains as the wedge evolves. The numerical estimates of work consumed by fault propagation overlap the range calculated from experimental force data, and crustal faults. The integration of numerical and physical experiments provides a powerful approach that demonstrates the utility of work optimization to predict the development of faults.

We present numerical models of faults propagating by work optimization in a homogeneous medium. These simulations allow quantification and comparison of the energy budgets of fault growth by shear versus tensile failure. The energy consumed by growth of a fault, Wgrow, propagating by in-line shearing is 76 % of the total energy associated with that growth, while 24 % is spent on frictional work during propagation. Wgrow for a fault propagating into intact rock by tensile failure, at an angle to the parent fault, consumes 60 % of the work budget, while only 6 % is consumed by frictional work associated with propagation. Following the conservation of energy, this leaves 34 % of the energy budget available for other activities and suggests that out-of-plane propagation of faults in Earth's crust may release energy for other processes, such as permanent damage zone formation or rupture acceleration. Comparison of these estimates of Wgrow with estimates of the critical energy release rate and earthquake fracture energy at several scales underscores their theoretical similarities and their dependence on stress drop.

Understanding the approach to faulting in continental rocks is critical for identifying processes leading to fracturing in geomaterials and the preparation process of large earthquakes. In situ dynamic X-ray imaging and digital volume correlation analysis of a crystalline rock core, under a constant confining pressure of 25 MPa, are used to elucidate the initiation, growth, and coalescence of microfractures leading to macroscopic failure as the axial compressive stress is increased. Following an initial elastic deformation, microfractures develop in the solid, and with increasing differential stress, the damage pervades the rock volume. The creation of new microfractures is accompanied by propagation, opening, and closing of existing microfractures, leading to the emergence of damage indices that increase as powers of the differential stress when approaching failure. A strong spatial correlation is observed between microscale zones with large positive and negative volumetric strains, microscale zones with shears of opposite senses, and microscale zones with high volumetric and shear strains. These correlations are attributed to microfracture interactions mediated by the heterogeneous stress field. The rock fails macroscopically as the microfractures coalesce and form a geometrically complex 3D volume that spans the rock sample. At the onset of failure, more than 70% of the damage volume is connected in a large fracture cluster that evolves into a fault zone. In the context of crustal faulting dynamics, these results suggest that evolving rock damage around existing locked or future main faults influences the localization process that culminates in large brittle rupture events.

Advances in triaxial compression deformation apparatus design, dynamic X-ray microtomography imaging, data analysis techniques, and digital volume correlation analysis provide unparalleled access to the in situ four-dimensional distribution of developing strain within rocks. To demonstrate the power of these new techniques and acquire detailed information about the micromechanics of damage evolution, deformation, and failure of porous rocks, we deformed 3-cm-scale cylindrical specimens of low-porosity Fontainebleau sandstone in an X-ray-transparent triaxial compression apparatus, and repeatedly recorded three-dimensional tomograms of the specimens as the differential stress was increased until macroscopic failure occurred. Experiments were performed at room temperature with confining pressure in the range of 10–20 MPa. Distinct grayscale subsets, indicative of density, enabled segmentation of the three-dimensional tomograms into intact rock matrix, pore space, and fractures. Digital volume correlation analysis of pairs of tomograms provided time series of three-dimensional incremental strain tensor fields throughout the experiments. After the yield stress was reached, the samples deformed first by dilatant opening and propagation of microfractures, and then by shear sliding via grain rotation and strain localization along faults. For two samples, damage and dilatancy occurred by grain boundary opening and then a sudden collapse of the granular rock framework at failure. For the third sample, a fault nucleated near the yield point and propagated in the sample through the development of transgranular microfractures. The results confirm findings of previous experimental studies on the same rock and provide new detailed quantifications of: (1) the proportion of shear versus dilatant strain in the sample, (2) the amount of dilatancy due to microfracture opening versus pore opening when a fault develops, and (3) the role of grain boundaries and pore walls in pinning microfracture propagation and slowing down the rate of damage accumulation as failure is approached. Our study demonstrates how the combination of high-resolution in situ dynamic X-ray microtomography imaging and digital volume image correlation analysis can be used to provide additional information to unravel brittle failure processes in rocks under stress conditions relevant to the upper crust.

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.

Tracking the evolution of the deformational energy budget within accretionary systems provides insight into the driving mechanisms that control fault development. To quantify the impact of these mechanisms on overall system efficiency, we estimate energy budget components as the first thrust fault pair develops in dry sand accretion experiments. We track energy budget components in experiments that include and exclude a basal layer of glass beads in order to investigate the influence of detachment strength on work partitioning. We use the measurements of normal force exerted on the backwall to estimate external work, and measurements of strain observed on the sides of the sandpacks to estimate the internal work, frictional work and work against gravity done within increments of each experiment. Thrust fault development reduces the incremental external work and incremental internal work, and increases the incremental frictional work and incremental gravitational work. The faults that develop within higher friction detachment experiments produce greater frictional work than the faults in experiments with glass bead detachments because the slip distribution along the detachments remain the same while the effective friction coefficient of the detachment differs between the experiments. The imbalance of the cumulative work budget suggests that additional deformational processes that are not fully captured in our measurements of the energy budget, such as acoustic energy, consume work within the deforming wedge.

Growth by Optimization of Work (GROW) is a new modeling tool that automates fracture initiation, propagation, interaction, and linkage. GROW predicts fracture growth by finding the propagation path and fracture geometry that optimizes the global external work of the system. This implementation of work optimization is able to simulate more complex paths of fracture growth than energy release rate methods. In addition, whereas a Coulomb stress analysis determines two conjugate planes of potential failure, GROW identifies a single failure surface for each increment of growth. GROW also eliminates ambiguity in determining whether shear or tensile failure will occur at a fracture tip by assessing both modes of failure by the same propagation criterion. Here we describe the underlying algorithm of the program and present GROW models of two propagating faults separated by a releasing step. The discretization error of these models demonstrates that GROW can predict fault propagation paths within the numerical uncertainty produced by discretization. Model element size moderately influences the propagation paths, however, the final fault geometry remains similar between models with significantly different element sizes. The propagation power of the fault system, calculated from the change in work due to fault propagation, indicates when model faults interact through both soft- and hard-linkage. First program to model fault growth through work optimization.Fault growth by work minimization as alternative to Coulomb failure planes.GROW models fault initiation, propagation and interactions.Work optimization detects soft- and hard-linkage.

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.

We investigate the scaling properties of the mechanical energy budget in accretionary prisms across five orders of magnitude, from the laboratory centimeter-scale to crustal kilometer-scale. We first develop numerical models that match the length scale, fault and material properties, surface topography, and fault geometries observed in scaled dry sand accretionary experiments. As we systematically increase the spatial dimensions of the numerical models by orders of magnitude, we calculate each component of the energy budget both before and after the first thrust fault pair develops. The increase of both the bulk stiffness and slip weakening distance from the laboratory- to crustal-scale produces a scale-invariant partitioning of the energy budget, relative to the total work done on the system. The components scale as power laws with exponents of three. Consequently, accurate laboratory simulations of the energetics of deformation within crustal accretionary wedges require careful scaling of the stiffness and slip weakening distance. Preceding thrust fault development at both the laboratory and crustal scale, the internal work consumes the largest portion of the budget (67-77%) and frictional work consumes the next largest portion (17-27%). Following thrusting, frictional work and internal work consume similar portions of the energy budget (38-50%). The sum of the remaining energy budget components, including gravitational work, seismic work, and the work of fracture propagation, consume

This study uses work optimization to predict the spatial and temporal development of faults. We focus on the growth of small fractures that develop into thrust faults at the toe of accretionary prisms because observations from physical laboratory accretion experiments provide rich data with which to validate the models, and the processes of accretionary thrust fault initiation remain unclear. In order to model these systems, we apply new implementations to the fault growth code GROW that improve its prediction of fault interaction using work optimization, including: 1) CPU parallelization, 2) a new growth algorithm that propagates only the most efficient fault in each growth increment, the single run mode, and 3) a new growth algorithm that only considers fault propagation from fault tips that host high sums of modes I and II stress intensity factors, KG, the limiting mode. The new single and limiting mode produce the geometries that best match the observed geometries, rather than the algorithm that allows all the faults to propagate simultaneously, regardless of KG, the multiple and non-limiting mode. The single limiting models predict that frontal accretionary thrusts initiate at the midpack or shallower depths, consistent with findings of previous studies. The thrusts propagate upward, link with the surface, and then propagate downward and link with the detachment. The backthrust tends to propagate before the forethrust, and then influences the forethrust propagation. This temporal and spatial sequence of faulting arises from the lower compression, higher shear strain, higher Coulomb stress and higher strain energy density that develop near the wedge surface and the inflection of the wedge slope. The models reveal that the final slip distributions do not reliably indicate the initiation location of the faults, in contrast to widespread assumptions.

The circum-Caloris geologic units show morphology consistent with ejecta-derived formation, however crater counts suggest the units formed after the basin. To determine if the surrounding units are directly related to basin formation or products of later volcanic resurfacing events, we measured the heights and densities of knobs in 22 study regions to the east of the Caloris basin in three geologic units circumferential to the basin: the Odin Formation, the Van Eyck Formation, and the Smooth Plains Formation. In these study regions the size and concentration of ejecta blocks generally decrease away from the crater rim. The morphology that superposes the knobs and the distribution of knob heights within each study region suggests that the knobs were deposited as ejecta and later embayed by one or multiple volcanic events. The distribution of knob height and concentration indicates that the knobs within the circum-Caloris units are related to the formation of the basin.