Abstract The brittle–ductile transition, typically located near the base of the seismogenic zone, controls strain localization and the evolution of physical properties, with direct implications for fluid transport and fault mechanics. However, quantitative constraints on strain partitioning and porosity evolution across this transition remain limited, particularly in low‐porosity carbonate rocks. We conducted triaxial compression experiments on dry Carrara marble at confining pressures of 5 and 100 MPa using two complementary techniques: (a) acoustic emission (AE) monitoring coupled with P‐wave velocity measurement, and (b) in situ X‐ray microtomography combined with digital volume correlation (DVC). AE activity remains low at all pressures, with source mechanisms becoming increasingly compaction‐dominated at the highest confinement. P‐wave velocities fall markedly during deformation by up to 60% at 5–10 MPa, ∼50% at 40 MPa, and ∼40% at 100 MPa, reflecting pervasive microcrack development. DVC reveals that the proportion of dilative volumetric strain decreases with confinement from nearly 90% at 5 MPa to 50% at 70–90 MPa, yet dilation remains a major component and is comparable to compaction even at the highest pressures. X‐ray–derived bulk porosity increases from <1% to ≈1.5% at low confinement prior to failure, and to 10% at higher confinements, indicating substantial porosity generation during distributed dilatant cataclastic flow. Together, these results provide the first quantitative link between P‐wave velocity reduction, volumetric strain partitioning, and transient porosity generation across the brittle to semi‐ductile transition, revealing how the interplay of dilation and compaction governs both elastic properties and strain localization in low‐porosity crystalline carbonate.

The dynamics of asperities and the resulting real contact area play an important role in the evolving frictional strength of fault zones, particularly during the interseismic period. The aperture of fractures controls the ability of fluids to traverse meaningful distances in geologically and industrially relevant timescales. Here, we show the evolution of the real contact area and aperture at increasing normal load in a triaxial compression experiment with X-ray tomography on a Westerly granite rock core with a preexisting core-spanning fracture oriented perpendicular to the maximum compressive principal stress direction, at a confining pressure of 15 MPa and fluid pressure of water of 10 MPa. At the onset of normal loading, the real contact area increases linearly with the differential stress, at a rate of about 0.2 %/MPa until the real contact area is 20 %, mostly though the accumulation of greater numbers of individual contacts, consistent with elastic deformation. Then the real contact area increases more rapidly with load, with increasing areas of individual contacts, consistent with plastic deformation. The real contact area reaches maximum values of 35 %, and then declines with increasing loading as secondary axial fractures propagate from the large sub-horizontal fracture. The average mechanical aperture first declines rapidly with loading, reaches a minimum value of 13 mu m, and then increases before failure as secondary axial fractures develop. The rough sub-horizontal fracture and secondary axial fractures produce a long-lived zone of elevated porosity, which is 4 % above the background porosity (1-2 %) just before failure. Thus, a closing rough fracture can provide a conduit for fluid flow due to non-zero aperture and the production of secondary damage.

Fracture development controls the conditions of catastrophic failure of rocks and other heterogeneous materials in the brittle regime. To characterize fracture development during the preparation process of failure, we calculate the volume of fractures propagating in isolation and fractures coalescing throughout eight triaxial compression experiments with in situ synchrotron X-ray microtomography acquisition. We track this behavior in experiments on Westerly granite at ambient temperature with varying confining pressure (5-20 MPa), and fluid pressure (0-10 MPa). In all of the experiments, the coalescing fracture porosity rapidly increases preceding macroscopic failure, on average at 97% of the failure stress. Fractures become increasingly parallel to the maximum compression direction with loading, and increasing volumes of coalescing fractures. The orientation of groups of fractures is more oblique to the maximum compression direction than the orientation of individual fractures, consistent with the development of faults from arrays of en echelon opening mode fractures. The volume of coalescing fractures at each stress increment is more strongly correlated with the volume of fractures with lengths greater than the mean grain size, i.e., the critical fractures, than with the volume of fractures with lengths greater than the spacing, L/S > 1, between fracture pairs. The mean grain size is thus a more robust metric of fracture network behavior than the spacing between fractures. Using a grain size of 1,025 mu m to identify the critical fractures produces the strongest correlations with the volume of coalescing fractures.

Rocks exhibit a brittle failure mode, leading to system-size failure through cataclastic faulting processes involving microfracture coalescence and frictional sliding, resulting in localized deformation. In contrast, the ductile failure mode can be described as a distributed deformation at the macroscopic scale, although there may be significant grain-scale heterogeneities. The transition between these two modes is an important research area because it is assumed to occur at the base of the seismogenic zone where large earthquakes may nucleate. Understanding strain evolution and partitioning between brittle and ductile failure modes may shed light on the preparation process for large earthquakes. To investigate the transition from brittle to ductile deformation, we performed two series of experiments on Carrara marble core samples: conventional triaxial experiments with acoustic emission recording at GFZ Potsdam, and dynamic in situ 4D X-ray imaging experiments on beamline BM18 at the European Synchrotron Radiation Facility. Carrara marble is used as a rock model because this transition can be achieved at room temperature. We performed the experiments at room temperature and confining pressures between 5 and 100 MPa. For the synchrotron experiments, we segmented the images and implemented digital volume correlation (DVC) analyses between tomogram acquisitions to quantify the evolution of volumetric and shear strain components during the transition from the brittle to ductile regime. The results show that the transition is controlled by the dynamics of microfractures, even in the ductile regime. Below 40 MPa of confining pressure, deformation localizes along faults, particularly at 5 and 10 MPa. At 40 MPa, tomograms reveal the formation of a localized shear zone and macroscopically distributed deformation, resembling a semi-brittle regime. The DVC reveals the spatial extent of the strain directed into faults. A limited number of acoustic emissions recorded at this confining pressure revealed the prevalence of aseismic activity during deformation. Above 40 MPa, deformation shifts to a non-localized pattern at the core sample scale, involving the opening of microfractures, possibly due to the cataclastic flow mechanism accommodating this regime.

Analyzing how fracture networks develop from preexisting isolated fault segments in immature faults may provide knowledge of the preparation process leading to fault growth and dynamic rupture. We reproduce this process experimentally using triaxial compression experiments coupled with time-lapse in-situ synchrotron X-ray tomography in Westerly granite core samples (10 mm diameter, 20 mm height) that contain two parallel notches oriented at 30 degrees with respect to the axis of the cylinder. We conducted the experiments at room temperature with a constant confining pressure of 20 MPa. We image microfracture development, characterize the microphysical processes of damage and fault growth in an intact rock bridge between the notches, and analyze the evolution of fractures oriented at 0 degrees-17 degrees (extensile) and 17 degrees-32 degrees (shear) as the rock approached failure. We also elucidate the strain localization process in the deforming rock using digital volume correlation. Our study offers a detailed comparison of microfracture and strain field development during fault growth. Results indicate that the rock bridge between the notches becomes damaged with a damage rate and a fracture rate diverging as the rock approaches macroscopic failure. Immediately preceding failure, shear fractures dominate the fracture networks. DVC analysis showed that the deformation process is mixed-mode, accommodated by dilation and shear strain, with the shear strains being more localized than the dilation. Furthermore, regions of high dilative strain host both extensile and shear fractures. These findings provide valuable insights into the fault growth process within an intact rock bridge between two fault segments in nature, demonstrating how mixed-mode deformation facilitates fault maturation.

Under compression in the brittle regime, rocks fail as fracture interaction, propagation and coalescence produce a process zone of high strains that forms the nucleus of the fault that eventually traverses the rock core. Early analyses suggested that this process zone extends through relatively intact rock close to the peak stress, and that the deformation that develops earlier in loading does not guide the location of this process zone. Here, we assess the predictability of the location of the process zone in triaxial compression experiments on Darley Dale sandstone. We develop supervised machine learning models to predict whether a particular location in the rock core will eventually host high shear and dilative strain, and thus eventually reside within the process zone. We calculate the local incremental strain tensors throughout the rock cores using digital volume correlation of X-ray tomograms captured during the experiments. We find that the models produce accuracies of 0.73 on average, indicating that it is possible to predict the location of the process zone using observations of the strain field preceding macroscopic failure. The average accuracy increases to 0.84 when the data are restricted to later in the experiment because the strain field becomes more similar to the final strain field that hosts the process zone. The models primarily rely on the shear strain field to predict the location of the process zone, likely because it is more spatially persistent than the dilative strain. The local neighbourhood of the strain field is helpful for predicting whether a location will eventually host the process zone only when the data are restricted to one experiment. When the data includes several experiments, the models primarily rely on global statistics of the strain fields. The varying correlation lengths of the dilative and shear strain field of different experiments help explain this result.

AbstractThe 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.

Shale lithofacies classification is one of the key components of shale reservoir evaluation. Typically, a significant amount of laboratory X-ray diffraction (XRD) data acquired on many shale samples collected in a large number of boreholes is required to constrain the mineral composition that enables classifying shale lithofacies at the basin scale. This procedure is costly and time consuming. Here, we propose a supervised machine learning method to predict the mineral composition of shale samples, including the clay and silicate content. The main advantage of our approach is that it only uses conventional logging data and a small number of XRD measurements of core samples, combined with XGBoost algorithm, to predict shale lithofacies, which can reduce the cost and improve the efficiency of reservoir evaluation. We apply our method on the early Permian shales in the Ordos Basin, China, because these shale rocks have a high potential of gas production. However, these formations are also highly heterogeneous, making them challenging to explore and exploit. Therefore, it is critical to perform detailed lithofacies classification analysis at the basin scale before gas production. Our result show that the gamma ray, neutron porosity, and density measurements are the critical logging data that control the model predictions. These parameters are known to be sensitive to clay content, thereby supporting the robustness of model predictions. Applying the model to different wells to classify shale lithofacies, results that these shale formations are dominated by three types of lithofacies. We characterize the different shale lithofacies by microscopy images and gas adsorption measurements, and demonstrate that our results are consistent with previous studies, verifying the accuracy and applicability of our machine learning method to classify shale lithofacies.

Previous studies show that the total volume of fractures increases non-linearly during loading as rocks approach failure in triaxial compression at stress and temperature conditions representative of the upper crust. However, the factors that control the critical volume of fractures or the critical spatial organization of the fracture network that trigger macroscopic failure remain unclear. To identify the fracture characteristics that determine the timing of macroscopic failure and localization of the fracture networks, we analyze data from six X-ray tomography experiments on Westerly granite with varying confining stress, fluid pressure, and amounts of preexisting damage. We develop machine learning models to predict 1) the timing of failure, 2) the localization of the fracture networks as measured with the Gini coefficient of the fracture volume, and 3) the change in localization from one differential stress step to the next. When the models only have access to individual fracture characteristics, the fracture length produces the best predictions of the distance to failure. When the models have access to the fracture length and sets of other characteristics, the fracture volume, aperture, and distance between fractures produce the best predictions of the distance to failure. The characteristics that describe the time or loading in the experiment, the axial strain and differential stress, produce some of the best predictions of the Gini coefficient. The results are generally consistent among the different experiments, suggesting that the fracture characteristics that determine the timing of macroscopic failure, and the localization of the fracture network, are independent of the range of confining stress, fluid pressure, and amount of preexisting damage tested here. Our results are consistent with the idea that monitoring the spatial distribution of deformation and changes in the seismic wave properties indicative of fracture growth may improve forecasting efforts of failure in the crust.

AbstractFracture networks in rocks and other geomaterials form by seismic and aseismic damage processes that could lead to system‐size failure. Here, we use a multi‐view convolutional neural network model to predict the stress proximity to macroscopic failure of experimentally deformed rock samples using two‐dimensional images. Models are trained on time series of fractures observed in rock samples through dynamic in situ synchrotron X‐ray tomography experiments. The results demonstrate that deep learning models outperform traditional estimates based on fracture density, increasing the accuracy of the predictions. Furthermore, the models provide insights into fundamental characteristics of fracture patterns that may provide precursory information on impending material failure. The trained deep learning models estimate the angle of the fracture plane relative to the principal loading direction, which is a key factor contributing to shear failure. The predicted angle of the fracture plane, in the range of 10°–30° with respect to the direction of maximum compressive stress, is consistent with the established failure criteria used in rock mechanics.

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.

SUMMARY Determining the size of the representative elementary volume (REV) for properties of fracture networks, such as porosity and permeability, is critical to robust upscaling of properties measured in the laboratory to crustal systems. Although fractured and damaged rock may have higher porosity and permeability than more intact rock, and thus exert a dominant influence on fluid flow, mechanical stability and seismic properties, many of the analyses that have constrained the REV size in geological materials have used intact rock. The REV size is expected to evolve as fracture networks propagate and coalesce, particularly when fracture development becomes correlated and the growth of one fracture influences the growth of another fracture. As fractures propagate and open with increasing differential stress, the REV size may increase to accommodate the larger fractures. The REV size may also increase as a consequence of the increasing heterogeneity of the fracture network, as many smaller fractures coalesce into fewer and longer fractures, and some smaller fractures stop growing. To quantify the evolving heterogeneity of fracture networks, we track the REV size of the porosity throughout eleven triaxial compression experiments under confining stresses of 5–35 MPa. Acquiring X-ray tomography scans after each increase of differential stress provides the evolving 3-D fracture network in four rock types: Carrara marble, Westerly granite, quartz monzonite and Fontainebleau sandstone. In contrast to expectations, the REV size does not systematically increase toward macroscopic failure in all of the experiments. Only one experiment on sandstone experiences a systematic increase in REV size because this rock contains significant porosity preceding loading, and it subsequently develops a localized fracture network that spans the core. The REV size may not systematically increase in most of the experiments because the highly heterogeneous porosity distributions cause the REV to become larger than the core. Consistent with this idea, when the rock does not have a REV, the fractures tend to be longer, thicker, more volumetric, and closer together than when the rock hosts a REV. Our estimates of the REV for the porosity of the sandstone are similar to previous work: about two to four times the mean grain diameter, or 0.5–1 mm. This agreement with previous work and the <15 per cent change in the REV size in two of the sandstone experiments suggests that when a system composed of sandstone does not host a localized, system-spanning fracture network, estimates of the REV derived from intact sandstone may be similar to estimates derived from damaged sandstone. Using the existing REV estimates derived from intact sandstone to simulations with more damaged crust, such as the damage zone adjacent to large crustal faults, will allow numerical models to robustly simulate increasingly complex crustal systems.

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.

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.

Previous studies show that the total volume of fractures increases non-linearly during macroscopic yielding as rocks approach failure in triaxial compression at the stress and temperature conditions of the upper crust. However, the factors that control the critical volume of fractures or the critical spatial organization of the fracture network that trigger failure remain unclear. To identify the fracture characteristics that determine the timing of macroscopic failure and localization of the fracture networks, we analyze data from six X-ray tomography experiments on Westerly granite with varying confining stress, fluid pressure, and amounts of preexisting damage. We develop machine learning models to predict 1) the timing of failure, 2) the localization of the fracture networks with the Gini coefficient of the fracture volume, and 3) the change in localization from one differential stress step to the next. When the models only have access to individual fracture characteristics, the fracture length produces the best predictions of the distance to failure. When the models have access to the fracture length and sets of other characteristics, the fracture volume, aperture, and distance between fractures produce the best predictions of the distance to failure. The characteristics that describe the time or loading in the experiment, the axial strain and differential stress, produce some of the best predictions of the Gini coefficient. The results are generally consistent among the different experiments, suggesting that the fracture characteristics that determine the timing of macroscopic failure, and the localization of the fracture network are independent of the range of confining stress, fluid pressure, and amount of preexisting damage tested here. Our results are consistent with the idea that monitoring the spatial distribution of deformation and changes in the seismic wave properties indicative of fracture growth may improve forecasting efforts of failure in the crust.

Understanding the mechanical behavior of rocks is crucial in subsurface activities, including storage of carbon dioxide and hydrogen gases, which both rely on shale caprocks as potential sealing barriers. Several current large-scale initiatives focus on potential carbon storage in North Sea aquifers. The Draupne Formation contains a series of shale layers interbedded with sandstone layers, the overall thickness of which varies in the range from tens to hundreds of meters. Injection of carbon dioxide into the underlying sandstone reservoirs leads to changes in the surrounding stress field, which can result in fault reactivation or the creation of microfractures, and thus, alter the performance of the shale caprock. Time-resolved microcomputed tomography (4D mu CT) has, in recent years, become a powerful technique for studying the mechanical properties of rocks under stress conditions similar to those prevailing in geological reservoirs. Here, we present results from experiments performed on Draupne shale using a triaxial rig combined with 4D mu CT based on synchrotron radiation. Detailed mechanical analysis of the tomography datasets by digital volume correlation reveals the three-dimensional pattern of the temporally evolving deformation field. Intermittent bursts of deformation at different locations within the specimen are observed, which eventu-ally evolve into a major fracture plane extending laterally across the whole sample. This study suggests that the pseudolinear-elastic-appearing behavior in the macroscopic stress-strain relationship previously reported for Draupne shale samples could consist of a series of irreversible processes occurring at various weak points within the sample. The combination of 4D mu CT imaging with strain analysis enables in situ investigations of deformation processes via quantification of shear and volumetric strains within the sample, thus providing an improved understanding of the fracture dynamics of shales.

Deformation localization is a widely observed, but rarely quantified process in the crust. Recent observations suggest that the localization of seismicity and fracture networks can help identify the approach to catastrophic failure. Here, we quantify the localization processes of the volumetric and deviatoric strain components in twelve triaxial compression experiments imaged with X-ray tomography. We capture three-dimensional images of the rock cores during triaxial compressing toward failure, and then calculate the local strain components using digital volume correlation. The divergence and curl of the incremental displacement vector field provide the volumetric and deviatoric components of the strain field. We quantify localization using the proportion of the rock occupied by high magnitudes of the volumetric and deviatoric strains, and the Gini coefficient of these high magnitude strains, which measures the deviation from a uniform process. We find that the vast majority, but not all, of the experiments experience strain localization toward failure. The rocks typically experience their maximum degree of strain localization not immediately preceding failure, but on average at 90% of the failure stress. The volumetric strain tends to localize more than the deviatoric strain. These observations support using the localization of the volumetric strain, along with the deviatoric strain, to identify the evolution of the precursory phase preceding earthquakes.

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 11 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 R 2 scores of >0.99, but predict the tortuosity with maximum R 2 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.

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), indicative of the shear strain. The importance of 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.