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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.

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.

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.